Publications

Anzahl der Treffer: 114
Erstellt: Thu, 28 Mar 2024 23:08:56 +0100 in 0.7007 sec


Goor, Pieter; vanMahony, Robert; Schaller, Manuel; Worthmann, Karl
Reprojection methods for Koopman-based modelling and prediction. - In: IEEE Xplore digital library, ISSN 2473-2001, (2023), S. 315-321

Extended Dynamic Mode Decomposition (eDMD) is a powerful tool to generate data-driven surrogate models for the prediction and control of nonlinear dynamical systems in the Koopman framework. In eDMD a compression of the lifted system dynamics on the space spanned by finitely many observables is computed, in which the original space is embedded as a low-dimensional manifold. While this manifold is invariant for the infinite-dimensional Koopman operator, this invariance is typically not preserved for its eDMD-based approximation. Hence, an additional (re-)projection step is often tacitly incorporated to improve the prediction capability. We propose a novel framework for consistent reprojectors respecting the underlying manifold structure. Further, we present a new geometric reprojector based on maximum-likelihood arguments, which significantly enhances the approximation accuracy and preserves known finite-data error bounds.



https://doi.org/10.1109/CDC49753.2023.10383796
Berger, Thomas; Lanza, Lukas
Funnel control of linear systems with arbitrary relative degree under output measurement losses. - In: IMA journal of mathematical control and information, ISSN 1471-6887, Bd. 40 (2023), 4, S. 691-713

We consider tracking control of linear minimum phase systems with known arbitrary relative degree which are subject to possible output measurement losses. We provide a control law which guarantees the evolution of the tracking error within a (shifted) prescribed performance funnel whenever the output signal is available. The result requires a maximal duration of measurement losses and a minimal time of measurement availability, which both strongly depend on the internal dynamics of the system, and are derived explicitly. The controller is illustrated by a simulation of a mass-on-car system.



https://doi.org/10.1093/imamci/dnad029
Schmitz, Philipp; Lanza, Lukas; Worthmann, Karl
Safe data-driven reference tracking with prescribed performance. - In: 2023 27th International Conference on System Theory, Control and Computing (ICSTCC), (2023), S. 454-460
ISBN 979-8-3503-3798-3

We study output reference tracking for unknown continuous-time systems with arbitrary relative degree. The control objective is to keep the tracking error within predefined time-varying bounds while measurement data is only available at discrete sampling times. To achieve the control objective, we propose a two-component controller. One part is a recently developed sampled-data zero-order hold controller, which achieves reference tracking within prescribed error bounds. To further improve the control signal, we explore the system dynamics via input-output data, and include as the second component a data-driven MPC scheme based on Willems et al.’s fundamental lemma. This combination yields significantly improved input signals as illustrated by a numerical example.



https://doi.org/10.1109/ICSTCC59206.2023.10308521
Hoffmann, Matthias K.; Esterhuizen, Willem; Worthmann, Karl; Flaßkamp, Kathrin
Path planning for concentric tube robots: a toolchain with application to stereotactic neurosurgery. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 56 (2023), 2, S. 2871-2876

We present a toolchain for solving path planning problems for concentric tube robots through obstacle fields. First, ellipsoidal sets representing the target area and obstacles are constructed from labelled point clouds. Then, the nonlinear and highly nonconvex optimal control problem is solved by introducing a homotopy on the obstacle positions where at one extreme of the parameter the obstacles are removed from the operating space, and at the other extreme they are located at their intended positions. We present a detailed example (with more than a thousand obstacles) from stereotactic neurosurgery with real-world data obtained from labelled MRI scans.



https://doi.org/10.1016/j.ifacol.2023.10.1403
Schaller, Manuel; Worthmann, Karl; Philipp, Friedrich; Peitz, Sebastian; Nüske, Feliks
Towards reliable data-based optimal and predictive control using extended DMD. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 56 (2023), 1, S. 169-174

While Koopman-based techniques like extended Dynamic Mode Decomposition are nowadays ubiquitous in the data-driven approximation of dynamical systems, quantitative error estimates were only recently established. To this end, both sources of error resulting from a finite dictionary and only finitely-many data points in the generation of the surrogate model have to be taken into account. We generalize the rigorous analysis of the approximation error to the control setting while simultaneously reducing the impact of the curse of dimensionality by using a recently proposed bilinear approach. In particular, we establish uniform bounds on the approximation error of state-dependent quantities like constraints or a performance index enabling data-based optimal and predictive control with guarantees.



https://doi.org/10.1016/j.ifacol.2023.02.029
Maschke, Bernhard; Kirchhoff, Jonas
Port maps of Irreversible Port Hamiltonian Systems. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 56 (2023), 2, S. 6796-6800

Irreversible Port Hamiltonian Systems are a deviation from Port Hamiltonian Systems which embeds the definition of the irreversible phenomena taking place in the system. They are defined with respect to a quasi-Poisson bracket which ensures the positiveness of the entropy generation and is expressed in terms of the total entropy of the system. The port maps, however, associated with the conjugated port variables, were poorly justified and lacked any physical characterization. In this paper, we suggest a novel definition of the port maps which allows to recover not only the energy balance equation (when the Hamiltonian equals the total energy of the system) but also a entropy balance equation including the irreversible entropy creation term at the interface (the port) of the system in addition to the entropy creation term due to internal irreversible phenomena.



https://doi.org/10.1016/j.ifacol.2023.10.388
Kirchhoff, Jonas; Maschke, Bernhard
On the generating functions of irreversible port-Hamiltonian systems. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 56 (2023), 2, S. 10447-10452

We study the geometric structure of the drift dynamics of Irreversible port-Hamiltonian systems. This drift dynamics is defined with respect to a product of Poisson brackets, reflecting the interconnection structure and the constitutive relations of the irreversible phenomena occuring in the system. We characterise this product of Poisson brackets using a covariant 4-tensor and an associated function. We derive various conditions for which this 4-tensor and the associated function may be reduced to a product of almost Poisson brackets.



https://doi.org/10.1016/j.ifacol.2023.10.1061
Grüne, Lars; Worthmann, Karl
Homogeneity for control systems in discrete time. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 56 (2023), 1, S. 385-390

Homogeneity, as a generalization of linearity to nonlinear systems, has proven to be a very powerful in systems and control. Nevertheless, only recently a notion of homogeneity was proposed for discrete-time control systems. However, this so-called D-Homogeneity directly couples the stability behaviour with the degree of homogeneity - in contrast to the continuous-time case. As an alternative, we propose the notion of S-Homogeneity, which avoids this coupling. S-Homogeneity uses a state-dependent time step that is compatible with sampling and discretization in time. We show that this concept preserves a contraction property and null-controllability for state-dependent sampling. For fixed sampling time, it yields (practical/semi-global) null controllability for sufficiently fast sampling, depending on the degree of homogeneity.



https://doi.org/10.1016/j.ifacol.2023.02.065
¸Sen, Gök¸cen Devlet; Schaller, Manuel; Worthmann, Karl
Stage-cost design for optimal and model predictive control of linear port-Hamiltonian systems: energy efficiency and robustness. - In: Proceedings in applied mathematics and mechanics, ISSN 1617-7061, Bd. 23 (2023), 4, e202300296, S. 1-9

We consider singular optimal control of port-Hamiltonian systems with minimal energy supply. We investigate the robustness of different stage-cost designs w.r.t. time discretization and show that alternative formulations that are equivalent in continuous time, differ strongly in view of discretization. Furthermore, we consider the impact of additional quadratic control regularization and demonstrate that this leads to a considerable increase in energy consumption. Then, we extend our results to the tracking problem within model predictive control and show that the intrinsic but singular choice of the cost functional as the supplied energy leads to a substantial improvement of the closed-loop performance.



https://doi.org/10.1002/pamm.202300296
Sauerteig, Philipp;
Optimisation-based control in electrical grids and epidemiology. - [Berlin] : epubli, 2023. - xiv, 172 Seiten
Technische Universität Ilmenau, Dissertation 2023

ISBN 978-3-7575-7548-9

Diese Arbeit ist im Rahmen des KONSENS Projektes, gefördert durch das Bundesministerium für Bildung und Forschung (BMBF), entstanden. Hauptziel des KONSENS Konsortiums war die Konsistente Optimierung uNd Stabilisierung Elektrischer NetzwerkSysteme. Im Verlaufe der COVID-19 Pandemie, hat das Konsortium jedoch seine Expertise in mathematischer Modellierung, (numerischer) Analyse sowie optimaler Regelung auch dafür genutzt, um den Einfluss von Gegenmaßnahmen zu evaluieren und geeignete Strategien zur Eindämmung der Ausbreitung der Krankheit zu entwickeln. Infolgedessen ist diese Arbeit in zwei Teile untergliedert: Teil I: Verteilte Optimierung und Regelung von Microgrids, Teil II: Koordination von Gegenmaßnahmen gegen die Ausbreitung von Infektionskrankheiten. Der Schlüssel, um diese augenscheinlich grundlegend unterschiedlichen Probleme mittels verwandter Methoden zu adressieren, liegt in der Allgemeingültigkeit optimierungsbasierter Ansätze. Wir formulieren mathematische Modelle, um die jeweilige Systemdynamik zu beschreiben – in Teil I handelt es sich dabei um Batteriedynamiken, in Teil II um die Ausbreitung infektiöser Krankheiten. Dynamische Modelle in Verbindung mit beispielsweise ökonomischen Zielstellungen führen auf Optimalsteuerungsprobleme (engl. optimal control problems (OCPs)). Mit allen OCPs in dieser Arbeit gehen inhärente Unsicherheiten einher wie zum Beispiel der unbekannte zukünftige Nettoverbrauch (Teil I) und die grundsätzliche Entwicklung der pandemischen Lage (Teil II). Diese OCPs werden numerisch gelöst, um optimale Strategien zu ermitteln. Eine naive Implementierung der ermittelten Steuerung über den gesamten Optimierungshorizont würde während des Prozesses neu gewonnene Informationen nicht berücksichtigen. Eine Methode, die diese stetig neu gewonnenen Informationen in den Regelungsentwurf mit einbezieht, stellt die so genannte modellprädiktive Regelung (engl. model predictive control (MPC)) dar. MPC ist eine bewährte Methode, um OCPs mit Zustands- und Eingangsbeschränkungen in Echtzeit zu lösen und wird in beiden Teilen dieser Arbeit eingesetzt. Deshalb wird die grundlegende Idee von MPC in einem vorbereitenden Abschnitt erläutert.



Faulwasser, Timm; Ou, Ruchuan; Pan, Guanru; Schmitz, Philipp; Worthmann, Karl
Behavioral theory for stochastic systems? A data-driven journey from Willems to Wiener and back again. - In: Annual reviews in control, ISSN 1872-9088, Bd. 55 (2023), S. 92-117

The fundamental lemma by Jan C. Willems and co-workers is deeply rooted in behavioral systems theory and it has become one of the supporting pillars of the recent progress on data-driven control and system analysis. This tutorial-style paper combines recent insights into stochastic and descriptor-system formulations of the lemma to further extend and broaden the formal basis for behavioral theory of stochastic linear systems. We show that series expansions - in particular Polynomial Chaos Expansions (PCE) of L2-random variables, which date back to Norbert Wiener’s seminal work - enable equivalent behavioral characterizations of linear stochastic systems. Specifically, we prove that under mild assumptions the behavior of the dynamics of the L2-random variables is equivalent to the behavior of the dynamics of the series expansion coefficients and that it entails the behavior composed of sampled realization trajectories. We also illustrate the short-comings of the behavior associated to the time-evolution of the statistical moments. The paper culminates in the formulation of the stochastic fundamental lemma for linear time-invariant systems, which in turn enables numerically tractable formulations of data-driven stochastic optimal control combining Hankel matrices in realization data (i.e. in measurements) with PCE concepts.



https://doi.org/10.1016/j.arcontrol.2023.03.005
Kleyman, Viktoria; Schaller, Manuel; Mordmüller, Mario; Wilson, Mitsuru; Brinkmann, Ralf; Worthmann, Karl; Müller, Matthias A.
State and parameter estimation for retinal laser treatment. - In: IEEE transactions on control systems technology, ISSN 1558-0865, Bd. 31 (2023), 3, S. 1366-1378

Adequate therapeutic retinal laser irradiation needs to be adapted to local absorption. This leads to time-consuming treatments as the laser power needs to be successively adjusted to avoid undertreatment and overtreatment caused by too low or too high temperatures. Closed-loop control can overcome this burden by means of temperature measurements. To allow for model predictive control schemes, the current state and the spot-dependent absorption need to be estimated. In this article, we thoroughly compare moving horizon estimator (MHE) and extended Kalman filter (EKF) designs for joint state and parameter estimation. We consider two different scenarios, the estimation of one or two unknown absorption coefficients. For one unknown parameter, both estimators perform very similarly. For two unknown parameters, we found that the MHE benefits from active parameter constraints at the beginning of the estimation, whereas after a settling time, both estimators perform again very similarly as long as the parameters are inside the considered parameter bounds.



https://doi.org/10.1109/TCST.2022.3228442
Caragea, Andrei; Lee, Dae Gwan; Philipp, Friedrich; Voigtlaender, Felix
A Balian-Low type theorem for Gabor Riesz sequences of arbitrary density. - In: Mathematische Zeitschrift, ISSN 1432-1823, Bd. 303 (2023), 2, 48, S. 1-22

https://doi.org/10.1007/s00209-022-03182-6
Aschenbruck, Tim; Dickert, Jörg; Esterhuizen, Willem; Filipecki, Bartosz; Grundel, Sara; Helmberg, Christoph; Ritschel, Tobias K. S.; Sauerteig, Philipp; Streif, Stefan; Wasserrab, Andreas; Worthmann, Karl
Hierarchical power systems: optimal operation using grid flexibilities. - Cham : Springer International Publishing, 2023. - 1 Online-Ressource (viii, 55 Seiten). - (SpringerBriefs in Energy) ISBN 978-3-031-25699-8

Introduction -- Preliminary theory -- Providing flexibility via residential batteries -- Flexibility in the distribution grid -- Security and stability on the transmission grid -- Implementation in the distribution grid and the microgrids -- Numerical example -- Conclusion.



https://doi.org/10.1007/978-3-031-25699-8
Philipp, Friedrich;
Relatively bounded perturbations of J-non-negative operators. - In: Complex analysis and operator theory, ISSN 1661-8262, Bd. 17 (2023), 1, 14, insges. 30 S.

We improve known perturbation results for self-adjoint operators in Hilbert spaces and prove spectral enclosures for diagonally dominant J-self-adjoint operator matrices. These are used in the proof of the central result, a perturbation theorem for J-non-negative operators. The results are applied to singular indefinite Sturm-Liouville operators with Lp-potentials. Known bounds on the non-real eigenvalues of such operators are improved.



https://doi.org/10.1007/s11785-022-01263-2
Lee, Dae Gwan; Philipp, Friedrich; Voigtlaender, Felix
A note on the invertibility of the Gabor frame operator on certain modulation spaces. - In: The journal of Fourier analysis and applications, ISSN 1531-5851, Bd. 29 (2023), 1, 3, S. 1-20

We consider Gabor frames generated by a general lattice and a window function that belongs to one of the following spaces: the Sobolev space $$V_1 = H^1(\mathbb {R}^d)$$, the weighted $$L^2$$-space $$V_2 = L_{1 + |x|}^2(\mathbb {R}^d)$$, and the space $$V_3 = \mathbb {H}^1(\mathbb {R}^d) = V_1 \cap V_2$$consisting of all functions with finite uncertainty product; all these spaces can be described as modulation spaces with respect to suitable weighted $$L^2$$spaces. In all cases, we prove that the space of Bessel vectors in $$V_j$$is mapped bijectively onto itself by the Gabor frame operator. As a consequence, if the window function belongs to one of the three spaces, then the canonical dual window also belongs to the same space. In fact, the result not only applies to frames, but also to frame sequences.



https://doi.org/10.1007/s00041-022-09980-0
Ilchmann, Achim; Kirchhoff, Jonas
Relative genericity of controllablity and stabilizability for differential-algebraic systems. - In: Mathematics of control, signals, and systems, ISSN 1435-568X, Bd. 35 (2023), 1, S. 45-76

https://doi.org/10.1007/s00498-022-00332-3
Viehweg, Johannes; Worthmann, Karl; Mäder, Patrick
Parameterizing echo state networks for multi-step time series prediction. - In: Neurocomputing, ISSN 1872-8286, Bd. 522 (2023), S. 214-228

Prediction of multi-dimensional time-series data, which may represent such diverse phenomena as climate changes or financial markets, remains a challenging task in view of inherent nonlinearities and non-periodic behavior In contrast to other recurrent neural networks, echo state networks (ESNs) are attractive for (online) learning due to lower requirements w.r.t.training data and computational power. However, the randomly-generated reservoir renders the choice of suitable hyper-parameters as an open research topic. We systematically derive and exemplarily demonstrate design guidelines for the hyper-parameter optimization of ESNs. For the evaluation, we focus on the prediction of chaotic time series, an especially challenging problem in machine learning. Our findings demonstrate the power of a hyper-parameter-tuned ESN when auto-regressively predicting time series over several hundred steps. We found that ESNs’ performance improved by 85.1%-99.8% over an already wisely chosen default parameter initialization. In addition, the fluctuation range is considerably reduced such that significantly worse performance becomes very unlikely across random reservoir seeds. Moreover, we report individual findings per hyper-parameter partly contradicting common knowledge to further, help researchers when training new models.



https://doi.org/10.1016/j.neucom.2022.11.044
Nüske, Feliks; Peitz, Sebastian; Philipp, Friedrich; Schaller, Manuel; Worthmann, Karl
Finite-data error bounds for Koopman-based prediction and control. - In: Journal of nonlinear science, ISSN 1432-1467, Bd. 33 (2023), 1, 14, S. 1-34

The Koopman operator has become an essential tool for data-driven approximation of dynamical (control) systems, e.g., via extended dynamic mode decomposition. Despite its popularity, convergence results and, in particular, error bounds are still scarce. In this paper, we derive probabilistic bounds for the approximation error and the prediction error depending on the number of training data points, for both ordinary and stochastic differential equations while using either ergodic trajectories or i.i.d. samples. We illustrate these bounds by means of an example with the Ornstein-Uhlenbeck process. Moreover, we extend our analysis to (stochastic) nonlinear control-affine systems. We prove error estimates for a previously proposed approach that exploits the linearity of the Koopman generator to obtain a bilinear surrogate control system and, thus, circumvents the curse of dimensionality since the system is not autonomized by augmenting the state by the control inputs. To the best of our knowledge, this is the first finite-data error analysis in the stochastic and/or control setting. Finally, we demonstrate the effectiveness of the bilinear approach by comparing it with state-of-the-art techniques showing its superiority whenever state and control are coupled.



https://doi.org/10.1007/s00332-022-09862-1
Dennstädt, Dario;
Towards Funnel MPC for nonlinear systems with relative degree two. - In: Extended abstracts presented at the 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022, (2022), S. 656-659

Funnel MPC, a novel Model Predictive Control (MPC) scheme, allows guaranteed output tracking of smooth reference signals with prescribed error bounds for nonlinear multi-input multi-output systems. To this end, the stage cost resembles the high-gain idea of funnel control. Without imposing additional output constraints or terminal conditions, the Funnel MPC scheme is initially and recursively feasible for systems with relative degree one and stable internal dynamics. Using an additional funnel for the derivative as a penalty term in the stage cost, these results can be also extended to single-input single-output systems with relative degree two.



https://doi.org/10.15495/EPub_UBT_00006809
Schaller, Manuel; Worthmann, Karl; Philipp, Friedrich; Peitz, Sebastian; Nüske, Feliks
A note on efficient and reliable prediction-based control in the Koopman framework. - In: Extended abstracts presented at the 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022, (2022), S. 584-587

Extended Dynamic Mode Decomposition, embedded in the Koopman framework, is a widely-applied technique to predict the evolution of an observable along the flow of a dynamical (control) system. However, despite its popularity, the error analysis for control systems is still fragmentary. Here, we provide a complete and rigorous analysis of the approximation error for control systems. To this end, the approximation error is split up according to its two sources of error: the finite dictionary size (projection) and the finite amount of i.i.d. data used to generate the surrogate model (estimation). Then, invoking - among others - finite-elements techniques and the Chebyshev inequality, probabilistic error bounds are derived. Finally, we demonstrate the applicability of the novel error bounds in optimal control with state and control constraints.



https://doi.org/10.15495/EPub_UBT_00006809
Philipp, Friedrich; Reis, Timo; Schaller, Manuel
Port-Hamiltonian system nodes. - In: Extended abstracts presented at the 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022, (2022), S. 441-444

We present a framework to formulate infinite dimensional port-Hamiltonian systems by means of system nodes, which provide a very general and powerful setting for unbounded input and output operators that appear, e.g., in the context of boundary control or observation. One novelty of our approach is that we allow for unbounded and not necessarily coercive Hamiltonian energies. To this end, we construct finite energy spaces to define the port-Hamiltonian dynamics and give an application in case of multiplication operator Hamiltonians where the Hamiltonian density does not need to be positive or bounded. In order to model systems involving differential operators on these finite energy spaces, we show that if the total mass w.r.t. the Hamiltonian density (and its inverse) is finite, one can define a unique weak derivative.



https://doi.org/10.15495/EPub_UBT_00006809
Worthmann, Karl; Hotz, Thomas
Verbund: 05M2018 - KONSENS : Schlussbericht : Förderzeitraum: 01.01.2018-30.06.2021. - Ilmenau : Technische Universität Ilmenau. - 1 Online-Ressource (16 Seiten, 450,82 KB)Förderkennzeichen BMBF 05M18SIA

https://edocs.tib.eu/files/e01fb23/1870887948.pdf
Baumann, Michael; Grüne, Lars; Jacob, Birgit; Worthmann, Karl
Extended abstracts presented at the 25th International Symposium on Mathematical Theory of Networks and Systems MTNS 2022 : held 12-16 September 2022 in Bayreuth, Germany. - Bayreuth : Universität Bayreuth, 2022. - 1 Online-Ressource

Foreword: After more than two years of limited social and scientific interactions due to the Covid-19 pandemic, it was a pleasure to welcome more than 300 participants in person and about 60 online participants at MTNS 2022 in Bayreuth. Submissions to MTNS 2022 were possible as extended abstracts and full papers. The accepted full papers that were presented at the conference are published in IFAC PapersOnline https://www.sciencedirect.com/journal/ifacpapersonline/vol/55/issue/30. In this volume you find the extended abstracts that were presented at the conference. Further, you also find the titles of the plenary and semi-plenary talks as well as their abstracts resp. links to the corresponding full papers. We hope you enjoy these abstracts and to see you in person at MTNS in the future. The Editors M. H. Baumann, L. Grüne, B. Jacob, and K. Worthmann



https://doi.org/10.15495/EPub_UBT_00006809
Berger, Thomas; Dennstädt, Dario; Ilchmann, Achim; Worthmann, Karl
Funnel model predictive control for nonlinear systems with relative degree one. - In: SIAM journal on control and optimization, ISSN 1095-7138, Bd. 60 (2022), 6, S. 3358-3383

We show that Funnel MPC, a novel model predictive control (MPC) scheme, allows tracking of smooth reference signals with prescribed performance for nonlinear multi-input multioutput systems of relative degree one with stable internal dynamics. The optimal control problem solved in each iteration of funnel MPC resembles the basic idea of penalty methods used in optimization. To this end, we present a new stage cost design to mimic the high-gain idea of (adaptive) funnel control. We rigorously show initial and recursive feasibility of funnel MPC without imposing terminal conditions or other requirements like a sufficiently long prediction horizon.



https://doi.org/10.1137/21M1431655
Faulwasser, Timm; Maschke, Bernhard; Philipp, Friedrich; Schaller, Manuel; Worthmann, Karl
Optimal control of port-Hamiltonian descriptor systems with minimal energy supply. - In: SIAM journal on control and optimization, ISSN 1095-7138, Bd. 60 (2022), 4, S. 2132-2158

We consider the singular optimal control problem of minimizing the energy supply of linear dissipative port-Hamiltonian descriptor systems. We study the reachability properties of the system and prove that optimal states exhibit a turnpike behavior with respect to the conservative subspace. Further, we derive a input-state turnpike toward a subspace for optimal control of port-Hamiltonian ordinary differential equations with a feed-through term and a turnpike property for the corresponding adjoint states toward zero. In an appendix we characterize the class of dissipative Hamiltonian matrices and pencils.



https://doi.org/10.1137/21M1427723
Grüne, Lars; Philipp, Friedrich; Schaller, Manuel
Strict dissipativity for generalized linear-quadratic problems in infinite dimensions. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 55 (2022), 30, S. 311-316

We analyze strict dissipativity of generalized linear quadratic optimal control problems on Hilbert spaces. Here, the term “generalized” refers to cost functions containing both quadratic and linear terms. We characterize strict pre-dissipativity with a quadratic storage function via coercivity of a particular Lyapunov-like quadratic form. Further, we show that under an additional algebraic assumption, strict pre-dissipativity can be strengthened to strict dissipativity. Last, we relate the obtained characterizations of dissipativity with exponential detectability.



https://doi.org/10.1016/j.ifacol.2022.11.071
Schmitz, Philipp; Engelmann, Alexander; Faulwasser, Timm; Worthmann, Karl
Data-driven MPC of descriptor systems: a case study for power networks. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 55 (2022), 30, S. 359-364

Recently, data-driven predictive control of linear systems has received wide-spread research attention. It hinges on the fundamental lemma by Willems et al. In a previous paper, we have shown how this framework can be applied to predictive control of linear time-invariant descriptor systems. In the present paper, we present a case study wherein we apply data-driven predictive control to a discrete-time descriptor model obtained by discretization of the power-swing equations for a nine-bus system. Our results show the efficacy of the proposed control scheme and they underpin the prospect of the data-driven framework for control of descriptor systems.



https://doi.org/10.1016/j.ifacol.2022.11.079
Maschke, Bernhard; Philipp, Friedrich; Schaller, Manuel; Worthmann, Karl; Faulwasser, Timm
Optimal control of thermodynamic port-Hamiltonian systems. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 55 (2022), 30, S. 55-60

We consider the problem of minimizing the entropy, energy, or exergy production for state transitions of irreversible port-Hamiltonian systems subject to control constraints. Via a dissipativity-based analysis we show that optimal solutions exhibit the manifold turnpike phenomenon with respect to the manifold of thermodynamic equilibria. We illustrate our analytical findings via numerical results for a heat exchanger.



https://doi.org/10.1016/j.ifacol.2022.11.028
Schaller, Manuel; Kleyman, Viktoria; Mordmüller, Mario; Schmidt, Christian; Wilson, Mitsuru; Brinkmann, Ralf; Müller, Matthias A.; Worthmann, Karl
Model predictive control for retinal laser treatment at 1 kHz. - In: Automatisierungstechnik, ISSN 2196-677X, Bd. 70 (2022), 11, S. 992-1002

Laser photocoagulation is a technique applied in the treatment of retinal disease, which is often done manually or using simple control schemes. We pursue an optimization-based approach, namely Model Predictive Control (MPC), to enforce bounds on the peak temperature and, thus, to ensure safety during the medical treatment procedure - despite the spot-dependent absorption of the tissue. The desired laser repetition rate of 1 kHz is renders the requirements on the computation time of the MPC feedback a major challenge. We present a tailored MPC scheme using parametric model reduction, an extended Kalman filter for the parameter and state estimation, and suitably tuned stage costs and verify its applicability both in simulation and experiments with porcine eyes. Moreover, we give some insight on the implementation specifically tailored for fast numerical computations.



https://doi.org/10.1515/auto-2022-0030
Faulwasser, Timm; Flaßkamp, Kathrin; Ober-Blöbaum, Sina; Schaller, Manuel; Worthmann, Karl
Manifold turnpikes, trims, and symmetries. - In: Mathematics of control, signals, and systems, ISSN 1435-568X, Bd. 34 (2022), 4, S. 759-788

Classical turnpikes correspond to optimal steady states which are attractors of infinite-horizon optimal control problems. In this paper, motivated by mechanical systems with symmetries, we generalize this concept to manifold turnpikes. Specifically, the necessary optimality conditions projected onto a symmetry-induced manifold coincide with those of a reduced-order problem defined on the manifold under certain conditions. We also propose sufficient conditions for the existence of manifold turnpikes based on a tailored notion of dissipativity with respect to manifolds. Furthermore, we show how the classical Legendre transformation between Euler-Lagrange and Hamilton formalisms can be extended to the adjoint variables. Finally, we draw upon the Kepler problem to illustrate our findings.



https://doi.org/10.1007/s00498-022-00321-6
Mühlenhoff, Julian; Körbner, Thorben; Miccoli, Giovanni; Keiner, Dörthe; Hoffmann, Matthias K.; Sauerteig, Philipp; Worthmann, Karl; Flaßkamp, Kathrin; Urbschat, Steffi; Oertel, Joachim; Sattel, Thomas
A manually actuated continuum robot research platform for deployable shape-memory curved cannulae in stereotactic neurosurgery. - In: ACTUATOR 2022: International Conference and Exhibition on New Actuator Systems and Applications, (2022), S. 10-13

In this paper, a research platform for concentric tube continuum robots is developed in order to enable advances in deploying curved cannulae for stereotactic neurosurgery. The system consists of a manually operated high-precision actuation apparatus and a photogrammetric system with measurement errors in the range of 100 micrometer. With this platform, previously planned curved paths can be analyzed ex-situ w.r.t., e.g., target precision, follow-the-leader-behavior, and hysteretic phenomena. Regarding research towards an in-vivo application in human brains, first tests with porcine brain cadavers inside an intraoperative CT are conducted in order to pave the way for histological as well as target reachability studies.



https://ieeexplore.ieee.org/document/9899155
Sauerteig, Philipp; Hoffmann, Matthias K.; Mühlenhoff, Julian; Miccoli, Giovanni; Keiner, Dörthe; Urbschat, Steffi; Oertel, Joachim; Sattel, Thomas; Flaßkamp, Kathrin; Worthmann, Karl
Optimal path planning for stereotactic neurosurgery based on an elastostatic cannula model. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 55 (2022), 20, S. 600-605

In this paper, we propose a path-planning problem for stereotactic neurosurgery using concentric tube robots. The main goal is to reach a given region of interest inside the brain, e.g. a tumor, starting from a feasible point on the skull with an ideally short path avoiding certain sensitive brain areas. To describe the shape of the entire cannula from an entry point to the point of interest we use an existing mechanical model for continuum robots. We show numerically that our approach enables the surgeon to reach areas within the brain that would be impossible with a straight cannula as it is currently state of the art.



https://doi.org/10.1016/j.ifacol.2022.09.161
Schaller, Manuel; Wilson, Mitsuru; Kleyman, Viktoria; Mordmüller, Mario; Brinkmann, Ralf; Müller, Matthias A.; Worthmann, Karl
Parameter estimation and model reduction for model predictive control in retinal laser treatment. - In: Control engineering practice, ISSN 1873-6939, Bd. 128 (2022), 105320

Laser photocoagulation is one of the most frequently used treatment approaches for retinal diseases such as diabetic retinopathy and macular edema. The use of model-based control, such as Model Predictive Control (MPC), enhances a safe and effective treatment by guaranteeing temperature bounds. In general, real-time requirements for model-based control designs are not met since the temperature distribution in the eye fundus is governed by a heat equation with a nonlinear parameter dependency. This issue is circumvented by representing the model by a lower-dimensional system which well-approximates the original model, including the parametric dependency. We combine a global-basis approach with the discrete empirical interpolation method, tailor its hyperparameters to laser photocoagulation, and show its superiority in comparison to a recently proposed method based on Taylor-series approximation. Its effectiveness is measured in computation time for MPC. We further present a case study to estimate the range of absorption parameters in porcine eyes, and by means of a theoretical and numerical sensitivity analysis we show that the sensitivity of the temperature increase is higher with respect to the absorption coefficient of the retinal pigment epithelium (RPE) than of the choroid’s.



https://doi.org/10.1016/j.conengprac.2022.105320
Sauerteig, Philipp; Esterhuizen, Willem; Wilson, Mitsuru; Ritschel, Tobias K. S.; Worthmann, Karl; Streif, Stefan
Model predictive control tailored to epidemic models. - In: 2022 European Control Conference (ECC), (2022), S. 743-748

We propose a model predictive control (MPC) approach for minimising the social distancing and quarantine measures during a pandemic while maintaining a hard infection cap. To this end, we study the admissible and the maximal robust positively invariant set (MRPI) of the standard SEIR compartmental model with control inputs. Exploiting the fact that in the MRPI all restrictions can be lifted without violating the infection cap, we choose a suitable subset of the MRPI to define terminal constraints in our MPC routine and show that the number of infected people decays exponentially within this set. Furthermore, under mild assumptions we prove existence of a uniform bound on the time required to reach this terminal region (without violating the infection cap) starting in the admissible set. The findings are substantiated based on a numerical case study.



https://doi.org/10.23919/ECC55457.2022.9838589
Kirchhoff, Jonas;
Linear port-Hamiltonian systems are generically controllable. - In: IEEE transactions on automatic control, ISSN 1558-2523, Bd. 67 (2022), 6, S. 3220-3222

The new concept of relative generic subsets is introduced. It is shown that the set of controllable linear finite-dimensional port-Hamiltonian systems is a relative generic subset of the set of all linear finite-dimensional port-Hamiltonian systems. This implies that a random, continuously distributed port-Hamiltonian system is almost surely controllable.



https://doi.org/10.1109/TAC.2021.3098176
Berger, Thomas; Dennstädt, Dario
Funnel MPC with feasibility constraints for nonlinear systems with arbitrary relative degree. - In: IEEE control systems letters, ISSN 2475-1456, Bd. 6 (2022), S. 2804-2809

We study tracking control for nonlinear systems with known relative degree and stable internal dynamics by the recently introduced technique of Funnel MPC. The objective is to achieve the evolution of the tracking error within a prescribed performance funnel. We propose a novel stage cost for Funnel MPC, extending earlier designs to the case of arbitrary relative degree, and show that the control objective as well as initial and recursive feasibility are always achieved - without requiring any terminal conditions or a sufficiently long prediction horizon. We only impose an additional feasibility constraint in the optimal control problem.



https://doi.org/10.1109/LCSYS.2022.3178478
Öztürk, Emrah; Rheinberger, Klaus; Faulwasser, Timm; Worthmann, Karl; Preißinger, Markus
Aggregation of demand-side flexibilities: a comparative study of approximation algorithms. - In: Energies, ISSN 1996-1073, Bd. 15 (2022), 7, 2501, S. 1-14

Traditional power grids are mainly based on centralized power generation and subsequent distribution. The increasing penetration of distributed renewable energy sources and the growing number of electrical loads is creating difficulties in balancing supply and demand and threatens the secure and efficient operation of power grids. At the same time, households hold an increasing amount of flexibility, which can be exploited by demand-side management to decrease customer cost and support grid operation. Compared to the collection of individual flexibilities, aggregation reduces optimization complexity, protects households' privacy, and lowers the communication effort. In mathematical terms, each flexibility is modeled by a set of power profiles, and the aggregated flexibility is modeled by the Minkowski sum of individual flexibilities. As the exact Minkowski sum calculation is generally computationally prohibitive, various approximations can be found in the literature. The main contribution of this paper is a comparative evaluation of several approximation algorithms in terms of novel quality criteria, computational complexity, and communication effort using realistic data. Furthermore, we investigate the dependence of selected comparison criteria on the time horizon length and on the number of households. Our results indicate that none of the algorithms perform satisfactorily in all categories. Hence, we provide guidelines on the application-dependent algorithm choice. Moreover, we demonstrate a major drawback of some inner approximations, namely that they may lead to situations in which not using the flexibility is impossible, which may be suboptimal in certain situations.



https://doi.org/10.3390/en15072501
Grundel, Sara; Heyder, Stefan; Hotz, Thomas; Ritschel, Tobias K. S.; Sauerteig, Philipp; Worthmann, Karl
How much testing and social distancing is required to control COVID-19? : some insight based on an age-differentiated compartmental model. - In: SIAM journal on control and optimization, ISSN 1095-7138, Bd. 60 (2022), 2, S. S145-S169

In this paper, we provide insights on how much testing and social distancing is required to control COVID-19. To this end, we develop a compartmental model that accounts for key aspects of the disease: incubation time, age-dependent symptom severity, and testing and hospitalization delays; the model's parameters are chosen based on medical evidence, and, for concreteness, adapted to the German situation. Then, optimal mass-testing and age-dependent social distancing policies are determined by solving optimal control problems both in open loop and within a model predictive control framework. We aim to minimize testing and/or social distancing until herd immunity sets in under a constraint on the number of available intensive care units. We find that an early and short lockdown is inevitable but can be slowly relaxed over the following months.



https://doi.org/10.1137/20M1377783
Grüne, Lars; Schaller, Manuel; Schiela, Anton
Efficient model predictive control for parabolic PDEs with goal oriented error estimation. - In: SIAM journal on scientific computing, ISSN 1095-7197, Bd. 44 (2022), 1, S. A471-A500

We show how a posteriori goal oriented error estimation can be used to efficiently solve the subproblems occurring in a model predictive control (MPC) algorithm. In MPC, only an initial part of a computed solution is implemented as a feedback, which motivates grid refinement particularly tailored to this context. To this end, we present a truncated cost functional as an objective for goal oriented adaptivity and prove under stabilizability assumptions that error indicators decay exponentially outside the support of this quantity. This leads to very efficient time and space discretizations for MPC, which we will illustrate by means of various numerical examples.



https://doi.org/10.1137/20M1356324
Schmitz, Philipp; Faulwasser, Timm; Worthmann, Karl
Willems' fundamental lemma for linear descriptor systems and its use for data-driven output-feedback MPC. - In: IEEE control systems letters, ISSN 2475-1456, Bd. 6 (2022), S. 2443-2448

In this letter we investigate data-driven predictive control of discrete-time linear descriptor systems. Specifically, we give a tailored variant of Willems' fundamental lemma, which shows that for descriptor systems the non-parametric modeling via a Hankel matrix requires less data compared to linear time-invariant systems without algebraic constraints. Moreover, we use this description to propose a data-driven framework for optimal control and predictive control of discrete-time linear descriptor systems. For the latter, we provide a sufficient stability condition for receding-horizon control before we illustrate our findings with an example.



https://doi.org/10.1109/LCSYS.2022.3161054
Babovsky, Hans; Bold, Lea
Balanced states and closure relations: the fluid dynamic limit of kinetic models. - Ilmenau : Technische Universität Ilmenau, Institut für Mathematik, 2022. - 1 Online-Ressource (20 Seiten). - (Preprint ; M22,03)

The paper is concerned with closure relations for moment hierarchies of gaskinetic systems in the uid dynamic limit. We develop the concept of balanced solutions which provides a more detailed description of kinetic solutions that the classical approaches. This allows to compare di_erent models in use like the nonlinear Boltzmann equation, its linearization, and the BGK model and their relation to the classical Navier-Stokes equations.



https://nbn-resolving.org/urn:nbn:de:gbv:ilm1-2022200188
Ilchmann, Achim; Witschel, Jonas; Worthmann, Karl
Model predictive control for singular differential-algebraic equations. - In: International journal of control, ISSN 1366-5820, Bd. 95 (2022), 8, S. 2141-2150

We study model predictive control for singular differential-algebraic equations with higher index. This is a novelty when compared to the literature where only regular differential-algebraic equations with additional assumptions on the index and/or controllability are considered. By regularisation techniques, we are able to derive an equivalent optimal control problem for an ordinary differential equation to which well-known model predictive control techniques can be applied. This allows the construction of terminal constraints and costs such that the origin is asymptotically stable w.r.t. the resulting closed-loop system.



https://doi.org/10.1080/00207179.2021.1900604
Mordmüller, Mario; Kleyman, Viktoria; Schaller, Manuel; Wilson, Mitsuru; Worthmann, Karl; Müller, Matthias A.; Brinkmann, Ralf
Towards model-based control techniques for retinal laser treatment using only one laser. - In: Opto-Acoustic Methods and Applications in Biophotonics V, (2021), S. 1192305-1-1192305-3

Repetitively applied laser pulses are used for tissue heating and temperature measurement. The potential of model-based control techniques for temperature regulation by adjusting the energy of the heating pulses is explored.



https://doi.org/10.1117/12.2615851
Sauerteig, Philipp; Baumann, Manuel; Dickert, Jörg; Grundel, Sara; Worthmann, Karl
Reducing transmission losses via reactive power control. - In: Mathematical modeling, simulation and optimization for power engineering and management, (2021), S. 219-232

Modern smart grids are required to transport electricity along transmission lines from the renewable energy sources to the customer’s demand in an efficient manner. It is inevitable that power is lost along these lines due to active as well as reactive power flows. However, the losses caused by reactive power flows can be reduced by optimizing the power factor. Therefore, we propose a power flow optimization problem aiming to reduce losses by controlling the power factors within the low-voltage electricity grid online. Furthermore, we show the potential of the proposed scheme in a numerical case study for two scenarios based on real-world data provided by a German distribution system operator.



Aschenbruck, Tim; Baumann, Manuel; Esterhuizen, Willem; Filipecki, Bartosz; Grundel, Sara; Helmberg, Christoph; Ritschel, Tobias K. S.; Sauerteig, Philipp; Streif, Stefan; Worthmann, Karl
Optimization and stabilization of hierarchical electrical networks. - In: Mathematical modeling, simulation and optimization for power engineering and management, (2021), S. 171-198

Triggered by the increasing number of renewable energy sources, the German electricity grid is undergoing a fundamental change from mono to bidirectional power flow. This paradigm shift confronts grid operators with new problems but also new opportunities. In this chapter we point out some of these problems arising on different layers of the grid hierarchy and sketch mathematical methods to handle them. While the transmission system operator’s main concern is stability and security of the system in case of contingencies, the distribution system operator aims to exploit inherent flexibilities. We identify possible interconnections among the layers to make the flexibility from the distribution grid available within the whole network. Our presented approaches include: the distributed control of energy storage devices on a residential level; transient stability analysis via a new set-based approach; a new clustering-based model-order reduction technique; and a modeling framework for the power flow problem on the transmission level which incorporates new grid technologies.



Mordmüller, Mario; Kleyman, Viktoria; Schaller, Manuel; Wilson, Mitsuru; Theisen-Kunde, Dirk; Worthmann, Karl; Müller, Matthias A.; Brinkmann, Ralf
Towards temperature controlled retinal laser treatment with a single laser at 10 kHz repetition rate. - In: Advanced Optical Technologies, ISSN 2192-8584, Bd. 10 (2021), 6, S. 423-431

Laser photocoagulation is one of the most frequently used treatment approaches in ophthalmology for a variety of retinal diseases. Depending on indication, treatment intensity varies from application of specific micro injuries down to gentle temperature increases without inducing cell damage. Especially for the latter, proper energy dosing is still a challenging issue, which mostly relies on the physician's experience. Pulsed laser photoacoustic temperature measurement has already proven its ability for automated irradiation control during laser treatment but suffers from a comparatively high instrumental effort due to combination with a conventional continuous wave treatment laser. In this paper, a simplified setup with a single pulsed laser at 10 kHz repetition rate is presented. The setup combines the instrumentation for treatment as well as temperature measurement and control in a single device. In order to compare the solely pulsed heating with continuous wave (cw) tissue heating, pulse energies of 4 [my]J were applied with a repetition rate of 1 kHz to probe the temperature rise, respectively. With the same average laser power of 60 mW an almost identical temporal temperature course was retrieved in both irradiation modes as expected. The ability to reach and maintain a chosen aim temperature of 41 ˚C is demonstrated by means of model predictive control (MPC) and extended Kalman filtering at a the measurement rate of 250 Hz with an accuracy of less than ±0.1 ˚C. A major advantage of optimization-based control techniques like MPC is their capability of rigorously ensuring constraints, e.g., temperature limits, and thus, realizing a more reliable and secure temperature control during retinal laser irradiation.



https://doi.org/10.1515/aot-2021-0041
Philipp, Friedrich; Schaller, Manuel; Faulwasser, Timm; Maschke, Bernhard; Worthmann, Karl
Minimizing the energy supply of infinite-dimensional linear port-Hamiltonian systems. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 54 (2021), 19, S. 155-160

We consider the problem of minimizing the supplied energy of infinite-dimensional linear port-Hamiltonian systems and prove that optimal trajectories exhibit the turnpike phenomenon towards certain subspaces induced by the dissipation of the dynamics. The theoretical foundations are illustrated by means of numerical examples concerning a Timoshenko beam and the heat equation.



https://doi.org/10.1016/j.ifacol.2021.11.071
Kleyman, Viktoria; Schaller, Manuel; Wilson, Mitsuru; Mordmüller, Mario; Brinkmann, Ralf; Worthmann, Karl; Müller, Matthias A.
State and parameter estimation for model-based retinal laser treatment. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 54 (2021), 6, S. 244-250

We present an approach for state and parameter estimation in retinal laser treatment by a novel setup where both measurement and heating is performed by a single laser. In this medical application, the temperature that is induced by the laser in the patients eye is critical for a successful and safe treatment. To this end, we pursue a model-based approach using a model given by a heat diffusion equation on a cylindrical domain, where the source term is given by the absorbed laser power. The model is parametric in the sense that it involves an absorption coefficient, which depends on the treatment spot and plays a central role in the input-output behavior of the system. After discretization, we apply a particularly suited parametric model order reduction to ensure real-time tractability while retaining parameter dependence. We augment known state estimation techniques, i.e., extended Kalman filtering and moving horizon estimation, with parameter estimation to estimate the absorption coefficient and the current state of the system. Eventually, we show first results for simulated and experimental data from porcine eyes. We find that, regarding convergence speed, the moving horizon estimation slightly outperforms the extended Kalman filter on measurement data in terms of parameter and state estimation, however, on simulated data the results are very similar.



https://doi.org/10.1016/j.ifacol.2021.08.552
Faulwasser, Timm; Grüne, Lars; Humaloja, Jukka-Pekka; Schaller, Manuel
Inferring the adjoint turnpike property from the primal turnpike property. - In: 60th IEEE Conference on Decision and Control, (2021), S. 2578-2583

This paper investigates an interval turnpike result for the adjoints/costates of finite- and infinite-dimensional nonlinear optimal control problems under the assumption of an interval turnpike on states and controls. We consider stabilizable dynamics governed by a generator of a semigroup with finite-dimensional unstable part satisfying a spectral decomposition condition and show the desired turnpike property under continuity assumptions on the first-order optimality conditions. We further provide a numerical example with a semilinear heat equation to illustrate the results.



https://doi.org/10.1109/CDC45484.2021.9683079
Grüne, Lars; Muff, David; Schaller, Manuel
Conditions for strict dissipativity of infinite-dimensional generalized linear-quadratic problems. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 54 (2021), 19, S. 302-306

We derive sufficient conditions for strict dissipativity for optimal control of linear evolution equations on Hilbert spaces with a cost functional including linear and quadratic terms. We show that strict dissipativity with a particular storage function is equivalent to ellipticity of a Lyapunov-like operator. Further we prove under a spectral decomposition assumption of the underlying generator and an orthogonality condition of the resulting subspaces that this ellipticity property holds under a detectability assumption. We illustrate our result by means of an example involving a heat equation on a one-dimensional domain.



https://doi.org/10.1016/j.ifacol.2021.11.094
Kleyman, Viktoria; Schaller, Manuel; Wilson, Mitsuru; Mordmüller, Mario; Brinkmann, Ralf; Worthmann, Karl; Müller, Matthias A.
Towards model-based temperature-control for retinal laser therapies. - In: Zenodo, (2021), insges. 2 S.

Sophisticated control designs for retinal laser therapies, such as model predictive control, allow for safer treatment and a uniform outcome irrespective of spatially varying parameters such as the absorption coefficient. To enable model-based control, the internal states and unknown parameters need to be estimated, which can be done using non-invasive temperature measurements. We present experimental results for joint state and parameter estimation using an extended Kalman filter and a moving horizon estimator. The experiments were conducted on ex vivo porcine eye's explants.



https://doi.org/10.5281/zenodo.4925803
Faulwasser, Timm; Mehrez, Mohamed; Worthmann, Karl
Predictive path following control without terminal constraints. - In: Recent advances in model predictive control, (2021), S. 1-26

Faulwasser, Timm; Flaßkamp, Kathrin; Ober-Blöbaum, Sina; Worthmann, Karl
A dissipativity characterization of velocity turnpikes in optimal control problems for mechanical systems. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 54 (2021), 9, S. 624-629

Turnpikes have recently gained significant research interest in optimal control, since they allow for pivotal insights into the structure of solutions to optimal control problems. So far, mainly steady state solutions which serve as optimal operation points, are studied. This is in contrast to time-varying turnpikes, which are in the focus of this paper. More concretely, we analyze symmetry-induced velocity turnpikes, i.e. controlled relative equilibria, called trim primitives, which are optimal operation points regarding the given cost criterion. We characterize velocity turnpikes by means of dissipativity inequalities. Moreover, we study the equivalence between optimal control problems and steady-state problems via the corresponding necessary optimality conditions. An academic example is given for illustration.



https://doi.org/10.1016/j.ifacol.2021.06.125
Rußwurm, Franz; Esterhuizen, Willem; Worthmann, Karl; Streif, Stefan
On MPC without terminal conditions for dynamic non-holonomic robots. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 54 (2021), 6, S. 133-138

We consider an input-constrained differential-drive robot with actuator dynamics. For this system, we establish asymptotic stability of the origin on arbitrary compact, convex sets using Model Predictive Control (MPC) without stabilizing terminal conditions despite the presence of state constraints and actuator dynamics. We note that the problem without those two additional ingredients was essentially solved beforehand, despite the fact that the linearization is not stabilizable. We propose an approach successfully solving the task at hand by combining the theory of barriers to characterize the viability kernel and an MPC framework based on so-called cost controllability. Moreover, we present a numerical case study to derive quantitative bounds on the required length of the prediction horizon. To this end, we investigate the boundary of the viability kernel and a neighbourhood of the origin, i.e. the most interesting areas.



https://doi.org/10.1016/j.ifacol.2021.08.535
Schaller, Manuel; Philipp, Friedrich; Faulwasser, Timm; Worthmann, Karl; Maschke, Bernhard
Control of port-Hamiltonian systems with minimal energy supply. - In: European journal of control, ISSN 1435-5671, Bd. 62 (2021), S. 33-40

We investigate optimal control of linear port-Hamiltonian systems with control constraints, in which one aims to perform a state transition with minimal energy supply. Decomposing the state space into dissipative and non-dissipative (i.e. conservative) subspaces, we show that the set of reachable states is bounded w.r.t. the dissipative subspace. We prove that the optimal control problem exhibits the turnpike property with respect to the non-dissipative subspace, i.e., for varying initial conditions and time horizons optimal state trajectories evolve close to the conservative subspace most of the time. We analyze the corresponding steady-state optimization problem and prove that all optimal steady states lie in the non-dissipative subspace. We conclude this paper by illustrating these results by a numerical example from mechanics.



https://doi.org/10.1016/j.ejcon.2021.06.017
Hackenberg, Annika; Worthmann, Karl; Pätz, Torben; Keiner, Dörthe; Oertel, Joachim; Flaßkamp, Kathrin
Neurochirurgische Planung mittels automatisierter Bilderkennung und optimaler Pfadplanung :
Neurosurgery planning based on automated image recognition and optimal path design. - In: Automatisierungstechnik, ISSN 2196-677X, Bd. 69 (2021), 8, S. 708-721

Stereotactic neurosurgery requires a careful planning of cannulae paths to spare eloquent areas of the brain that, if damaged, will result in loss of essential neurological function such as sensory processing, linguistic ability, vision, or motor function. We present an approach based on modelling, simulation, and optimization to set up a computational assistant tool. Thereby, we focus on the modeling of the brain topology, where we construct ellipsoidal approximations of voxel clouds based on processed MRI data. The outcome is integrated in a path-planning problem either via constraints or by penalization terms in the objective function. The surgical planning problem with obstacle avoidance is solved for different types of stereotactic cannulae using numerical simulations. We illustrate our method with a case study using real MRI data.



https://doi.org/10.1515/auto-2021-0044
Jiang, Yuning; Sauerteig, Philipp; Houska, Boris; Worthmann, Karl
Distributed optimization using ALADIN for MPC in smart grids. - In: IEEE transactions on control systems technology, ISSN 1558-0865, Bd. 29 (2021), 5, S. 2142-2152

This article presents a distributed optimization algorithm tailored to solve optimization problems arising in smart grids. In detail, we propose a variant of the augmented Lagrangian-based alternating direction inexact Newton (ALADIN) method, which comes along with global convergence guarantees for the considered class of linear-quadratic optimization problems. We establish local quadratic convergence of the proposed scheme and elaborate its advantages compared with the alternating direction method of multipliers (ADMM). In particular, we show that, at the cost of more communication, ALADIN requires fewer iterations to achieve the desired accuracy. Furthermore, it is numerically demonstrated that the number of iterations is independent of the number of subsystems. The effectiveness of the proposed scheme is illustrated by running both an ALADIN and an ADMM-based model predictive controller on a benchmark case study.



https://doi.org/10.1109/TCST.2020.3033010
Grundel, Sara; Heyder, Stefan; Hotz, Thomas; Ritschel, Tobias K. S.; Sauerteig, Philipp; Worthmann, Karl
How to coordinate vaccination and social distancing to mitigate SARS-CoV-2 outbreaks. - In: SIAM journal on applied dynamical systems, ISSN 1536-0040, Bd. 20 (2021), 2, S. 1135-1157

Most countries have started vaccinating people against COVID-19. However, due to limited production capacities and logistical challenges it will take months/years until herd immunity is achieved. Therefore, vaccination and social distancing have to be coordinated. In this paper, we provide some insight on this topic using optimization-based control on an age-differentiated compartmental model. For real-life decision-making, we investigate the impact of the planning horizon on the optimal vaccination/social distancing strategy. We find that in order to reduce social distancing in the long run, without overburdening the health care system, it is essential to vaccinate the people with the highest contact rates first. That is also the case if the objective is to minimize fatalities provided that the social distancing measures are sufficiently strict. However, for short-term planning it is optimal to focus on the high-risk group.



https://doi.org/10.1137/20M1387687
Grüne, Lars; Schaller, Manuel; Schiela, Anton
Abstract nonlinear sensitivity and turnpike analysis and an application to semilinear parabolic PDEs. - In: Control, optimisation and calculus of variations, ISSN 1262-3377, Bd. 27 (2021), 56, insges. 28 S.

We analyze the sensitivity of the extremal equations that arise from the first order necessary optimality conditions of nonlinear optimal control problems with respect to perturbations of the dynamics and of the initial data. To this end, we present an abstract implicit function approach with scaled spaces. We will apply this abstract approach to problems governed by semilinear PDEs. In that context, we prove an exponential turnpike result and show that perturbations of the extremal equation's dynamics, e.g., discretization errors decay exponentially in time. The latter can be used for very efficient discretization schemes in a Model Predictive Controller, where only a part of the solution needs to be computed accurately. We showcase the theoretical results by means of two examples with a nonlinear heat equation on a two-dimensional domain.



https://doi.org/10.1051/cocv/2021030
Faulwasser, Timm; Müller, Matthias A.; Worthmann, Karl
Recent advances in model predictive control : theory, algorithms, and applications. - Cham, Switzerland : Springer, 2021. - ix, 244 Seiten. - (Lecture notes in control and information sciences ; volume 485) ISBN 978-3-030-63280-9

Esterhuizen, Willem; Worthmann, Karl; Streif, Stefan
Recursive feasibility of continuous-time model predictive control without stabilising constraints. - In: IEEE control systems letters, ISSN 2475-1456, Bd. 5 (2021), 1, S. 265-270

https://doi.org/10.1109/LCSYS.2020.3001514
Sauerteig, Philipp; Jiang, Yuning; Houska, Boris; Worthmann, Karl
Distributed control enforcing group sparsity in smart grids. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 53 (2020), 2, S. 13269-13274

In modern smart grids, charging of local energy storage devices is coordinated within the distribution grid to compensate the volatile aggregated power demand on the time interval of interest. However, this results in a perpetual usage of all batteries which in return reduces their lifetime. In this paper, we enforce group sparsity by using an lp,q-regularization on the control to counteract this phenomenon. This leads to a non-smooth convex optimization problem, for which a tailored Alternating Direction Method of Multipliers algorithm is proposed. Furthermore, the algorithm is embedded in a Model Predictive Control framework. Numerical simulations show that the proposed scheme yields sparse control while achieving reasonable overall peak shaving.



https://doi.org/10.1016/j.ifacol.2020.12.156
Berger, Thomas; Kästner, Carolin; Worthmann, Karl
Learning-based funnel-MPC for output-constrained nonlinear systems. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 53 (2020), 2, S. 5177-5182

We exploit an adaptive control technique, namely funnel control, to establish both initial and recursive feasibility in Model Predictive Control (MPC) for output-constrained nonlinear systems. Moreover, we show that the resulting feedback controller outperforms the funnel controller both w.r.t. the required sampling rate for a zero-order-hold implementation and required control action. We further propose a combination of funnel control and MPC, exploiting the performance guarantees of the model-free funnel controller during a learning phase and the advantages of the model-based MPC scheme thereafter.



https://doi.org/10.1016/j.ifacol.2020.12.1186
Kleyman, Viktoria; Abbas, Hossam S.; Brinkmann, Ralf; Worthmann, Karl; Müller, Matthias A.
Modelling of heat diffusion for temperature-controlled retinal photocoagulation. - In: Proceedings on automation in medical engineering, Vol. 1 (2020), no. 1, paperID: 006, 2 Seiten

https://doi.org/10.18416/AUTOMED.2020
Coron, Jean-Michel; Grüne, Lars; Worthmann, Karl
Model predictive control, cost controllability, and homogeneity. - In: SIAM journal on control and optimization, ISSN 1095-7138, Bd. 58 (2020), 5, S. 2979-2996

We are concerned with the design of Model Predictive Control (MPC) schemes such that asymptotic stability of the resulting closed loop is guaranteed - even if the linearization at the desired set point fails to be stabilizable. Therefore, we propose constructing the stage cost based on the homogeneous approximation and rigorously show that applying MPC yields an asymptotically stable closed-loop behavior if the homogeneous approximation is asymptotically null controllable. To this end, we verify cost controllability - a condition relating the current state, the stage cost, and the growth of the value function with respect to time - for this class of systems in order to provide stability and performance guarantees for the proposed MPC scheme without stabilizing terminal costs or constraints.



https://doi.org/10.1137/19M1265995
Faulwasser, Timm; Göttlich, Simone; Worthmann, Karl
Mathematical innovations fostering the energy transition - control and optimization. - In: Automatisierungstechnik, ISSN 2196-677X, Bd. 68 (2020), 12, S. 982-984

https://doi.org/10.1515/auto-2020-0152
Kleyman, Viktoria; Gernandt, Hannes; Worthmann, Karl; Abbas, Hossam S.; Brinkmann, Ralf; Müller, Matthias A.
Modellierung und Parameteridentifikation für die Echtzeittemperaturregelung bei retinalen Lasertherapien :
Modeling and parameter identification for real-time temperature controlled retinal laser therapies. - In: Automatisierungstechnik, ISSN 2196-677X, Bd. 68 (2020), 11, S. 953-966

Laser photocoagulation is a widely used treatment for a variety of retinal diseases. Temperature-controlled irradiation is a promising approach to enable uniform heating, reduce the risks of over- or undertreatment, and unburden the ophthalmologists from a time consuming manual power titration. In this paper, an approach is proposed for the development of models with different levels of detail, which serve as a basis for improved, more accurate observer and control designs. To this end, we employ a heat diffusion model and propose a suitable discretization and subsequent model reduction procedures. Since the absorption of the laser light can vary strongly at each irradiation site, a method for identifying the absorption coefficient is presented. To identify a parameter in a reduced order model, an optimal interpolatory projection method for parametric systems is used. In order to provide an online identification of the absorption coefficient, we prove and exploit monotonicity of the parameter influence.



https://doi.org/10.1515/auto-2020-0074
Mehrez, Mohamed W.; Worthmann, Karl; Cenerini, Joseph P. V.; Osman, Mostafa; Melek, William W.; Jeon, Soo
Model predictive control without terminal constraints or costs for holonomic mobile robots. - In: Robotics and autonomous systems, ISSN 1872-793X, Bd. 127 (2020), 103468

https://doi.org/10.1016/j.robot.2020.103468
Sauerteig, Philipp; Worthmann, Karl
Towards multiobjective optimization and control of smart grids. - In: Optimal control, applications and methods, ISSN 1099-1514, Bd. 41 (2020), 1, S. 128-145

https://doi.org/10.1002/oca.2532
Braun, Philipp; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl
Towards price-based predictive control of a small-scale electricity network. - In: International journal of control, ISSN 1366-5820, Bd. 93 (2020), 1, S. 40-61

https://doi.org/10.1080/00207179.2017.1339329
Faulwasser, Timm; Flaßkamp, Kathrin; Ober-Blöbaum, Sina; Worthmann, Karl
Towards velocity turnpikes in optimal control of mechanical systems. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 52 (2019), 16, S. 490-495

https://doi.org/10.1016/j.ifacol.2019.12.009
Grundel, Sara; Sauerteig, Philipp; Worthmann, Karl
Surrogate models for coupled microgrids. - In: Progress in industrial mathematics at ECMI 2018, (2019), S. 477-483

https://doi.org/10.1007/978-3-030-27550-1_60
Braun, Philipp; Sauerteig, Philipp; Worthmann, Karl
Distributed optimization based control on the example of microgrids. - In: Computational intelligence and optimization methods for control engineering, (2019), S. 173-200

https://doi.org/10.1007/978-3-030-25446-9_8
Baumann, Manuel; Grundel, Sara; Sauerteig, Philipp; Worthmann, Karl
Ersatzmodelle in bidirektionaler Optimierung gekoppelter Microgrids :
Surrogate models in bidirectional optimization of coupled microgrids. - In: Automatisierungstechnik, ISSN 2196-677X, Bd. 67 (2019), 12, S. 1035-1046

https://doi.org/10.1515/auto-2019-0075
Flaßkamp, Kathrin; Ober-Blöbaum, Sina; Worthmann, Karl
Symmetry and motion primitives in model predictive control. - In: Mathematics of control, signals, and systems, ISSN 1435-568X, Bd. 31 (2019), 4, S. 455-485

https://doi.org/10.1007/s00498-019-00246-7
Flaßkamp, Kathrin; Worthmann, Karl; Mühlenhoff, Julian; Greiner-Petter, Christoph; Büskens, Christof; Oertel, Joachim; Keiner, Dörthe; Sattel, Thomas
Towards optimal control of concentric tube robots in stereotactic neurosurgery. - In: Mathematical and computer modelling of dynamical systems, ISSN 1744-5051, Bd. 25 (2019), 6, S. 560-574

https://doi.org/10.1080/13873954.2019.1690004
Ilchmann, Achim; Leben, Leslie; Witschel, Jonas; Worthmann, Karl
Optimal control of differential-algebraic equations from an ordinary differential equation perspective. - In: Optimal control, applications and methods, ISSN 1099-1514, Bd. 40 (2019), 2, S. 351-366

https://doi.org/10.1002/oca.2481
Ilchmann, Achim; Witschel, Jonas; Worthmann, Karl
Model predictive control for linear DAEs without terminal constraints and costs. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 51 (2018), 20, S. 116-121

https://doi.org/10.1016/j.ifacol.2018.11.002
Schulze Darup, Moritz; Worthmann, Karl
Tailored MPC for mobile robots with very short prediction horizons. - In: 2018 European Control Conference (ECC), (2018), S. 1361-1366

https://doi.org/10.23919/ECC.2018.8550514
Ilchmann, Achim; Witschel, Jonas; Worthmann, Karl
Model predictive control for linear differential-algebraic equations. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 51 (2018), 20, S. 98-103

https://doi.org/10.1016/j.ifacol.2018.10.181
Kurz, Sascha; Stoll, Michael; Worthmann, Karl
Angewandte Mathematik : Ein Lehrbuch für Lehramtsstudierende. - Berlin, Heidelberg : Springer Spektrum, 2018. - Online-Ressource (XVIII, 211 S. 15 Abb., 11 Abb. in Farbe, online resource). - (SpringerLink) ISBN 978-3-662-56705-0

Mathematik! Aber wozu soll das bitte gut sein? Fast jede Lehrerin und jeder Lehrer wurde bereits mit dieser Frage konfrontiert. Dieses Buch macht den (Mehr-)Wert von Mathematik erfahrbar, indem Sie Algorithmen kennenlernen, mit denen Sie eine Vielzahl praktisch relevanter Probleme lösen können. Aufbauend auf Grundkenntnissen der Analysis und linearen Algebra unternehmen wir einen Streifzug durch die Angewandte Mathematik: Angefangen mit dem Lösen linearer und nichtlinearer Gleichungssysteme über die lineare Optimierung bis hin zu modernen Verfahren der Computeralgebra. So finden Sie leicht ein passendes Thema, um die Lebenswelt Ihrer Schülerinnen und Schüler aktiv mit mathematischen Methoden zu verknüpfen: Sei es, indem Sie die Bevölkerungsentwicklung basierend auf realen Daten prognostizieren oder wirtschaftliche Prozesse optimieren. Oder auch, indem Sie vermeintlich altbekannte Aufgaben wie die Multiplikation so lange kneten, bis Sie und Ihr Computer sie wirklich schnell und effizient lösen. So bekommen Sie unter anderem neue Impulse für Schwerpunktthemen oder Facharbeiten. Die Autoren Sascha Kurz ist Professor (apl.) für Mathematik an der Universität Bayreuth und interessiert sich unter anderem für Algorithmen und diskrete Strukturen in Anwendungen wie Kodierungstheorie oder Abstimmungsverfahren. Michael Stoll ist Professor für Computeralgebra an der Universität Bayreuth und befasst sich in seiner Forschung neben anderen Dingen mit Lösungsverfahren für Diophantische Gleichungen. Karl Worthmann ist Juniorprofessor für Differentialgleichungen an der Technischen Universität Ilmenau und forscht unter anderem zu optimierungsbasierten Verfahren der Steuerung und Regelung mit Anwendungen für mobile Roboter oder den Einsatz erneuerbarer Energien



http://dx.doi.org/10.1007/978-3-662-56705-0
Sprodowski, Tobias; Mehrez, Mohamed W.; Worthmann, Karl; Mann, George K. I.; Gosine, Raymond G.; Sagawa, Juliana K.; Pannek, Jürgen
Differential communication with distributed MPC based on occupancy grid. - In: Information sciences, ISSN 0020-0255, Bd. 453 (2018), S. 426-441

https://doi.org/10.1016/j.ins.2018.04.034
Flaßkamp, Kathrin; Worthmann, Karl; Greiner-Petter, Christoph; Büskens, Christof; Sattel, Thomas
An optimal control problem for stereotactic neurosurgery. - In: MATHMOD 2018 extended abstract volume, (2018), S. 67-68

https://doi.org/10.11128/arep.55.a55246
Braun, Philipp; Faulwasser, Timm; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl
Hierarchical distributed ADMM for predictive control with applications in power networks. - In: IFAC journal of systems and control, ISSN 2468-6018, Bd. 3 (2018), S. 10-22

https://doi.org/10.1016/j.ifacsc.2018.01.001
Müller, Matthias A.; Worthmann, Karl
On quadratic stage costs for mobile robots in model predictive control. - In: Proceedings in applied mathematics and mechanics, ISSN 1617-7061, Bd. 17 (2017), 1, S. 825-826

https://doi.org/10.1002/pamm.201710380
Bergmann, Jean Pierre; Bielenin, Martin; Herzog, Roland A.; Hildebrand, Jörg; Riedel, Ilka; Schricker, Klaus; Trunk, Carsten; Worthmann, Karl
Prevention of solidification cracking during pulsed laser beam welding. - In: Proceedings in applied mathematics and mechanics, ISSN 1617-7061, Bd. 17 (2017), 1, S. 405-406

https://doi.org/10.1002/pamm.201710172
Mehrez, Mohamed W.; Sprodowski, Tobias; Worthmann, Karl; Mann, George K. I.; Gosine, Raymond G.; Sagawa, Juliana K.; Pannek, Jürgen
Occupancy grid based distributed MPC for mobile robots. - In: IROS Vancouver 2017, (2017), S. 4842-4847

https://doi.org/10.1109/IROS.2017.8206360
Mehrez, Mohamed W.; Worthmann, Karl; Mann, George K.I.; Gosine, Raymond G.; Pannek, Jürgen
Experimental speedup and stability validation for multi-step MPC. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 50 (2017), 1, S. 8698-8703

https://doi.org/10.1016/j.ifacol.2017.08.1551
Mehrez, Mohamed W.; Worthmann, Karl; Mann, George K.I.; Gosine, Raymond G.; Faulwasser, Timm
Predictive path following of mobile robots without terminal stabilizing constraints. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 50 (2017), 1, S. 9852-9857

https://doi.org/10.1016/j.ifacol.2017.08.907
Ioan, Daniel-Mihail; Stoican, Florin; Worthmann, Karl
Active fault detection and isolation in a zonotopic framework. - In: 2017 21st International Conference on System Theory, Control and Computing (ICSTCC), ISBN 978-1-5386-3842-2, (2017), S. 595-600

https://doi.org/10.1109/ICSTCC.2017.8107100
Bergmann, Jean Pierre; Bielenin, Martin; Herzog, Roland A.; Hildebrand, Jörg; Riedel, Ilka; Schricker, Klaus; Trunk, Carsten; Worthmann, Karl
Prevention of solidification cracking during pulsed laser beam welding. - Ilmenau : Technische Universität, Institut für Mathematik, 2017. - 1 Online-Ressource (7 Seiten). - (Preprint ; M17,09)

We present a mathematical model to describe laser beam welding based on the heat equation. Since the material coeff cients depend on the temperature, this leads to a quasi-linear parabolic partial differential equation. It is our goal to prevent solidif cation cracking. We address this problem by means of optimal control. It is the intensity prof le of the laser beam which acts as the control function. The main challenge is the formulation of a suitable objective function. In particular, high velocities of the solidif cation interface need to be properly penalized in order to deal with and avoid cracking phenomena.



https://www.db-thueringen.de/receive/dbt_mods_00032771
Worthmann, Karl; Mehrez, Mohamed W.; Mann, George K. I.; Gosine, Raymond G.; Pannek, Jürgen
Interaction of open and closed loop control in MPC. - In: Automatica, ISSN 0005-1098, Bd. 82 (2017), S. 243-250

https://doi.org/10.1016/j.automatica.2017.04.038
Müller, Matthias A.; Worthmann, Karl
Quadratic costs do not always work in MPC. - In: Automatica, ISSN 0005-1098, Bd. 82 (2017), S. 269-277

https://doi.org/10.1016/j.automatica.2017.04.058
Proch, Michael; Worthmann, Karl; Schlüchtermann, Jörg
A negotiation-based algorithm to coordinate supplier development in decentralized supply chains. - In: European journal of operational research, ISSN 0377-2217, Bd. 256 (2017), 2, S. 412-429

http://dx.doi.org/10.1016/j.ejor.2016.06.029
Braun, Philipp; Faulwasser, Timm; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl
Maximal islanding time for microgrids via distributed predictive control. - In: 22nd International Symposium on Mathematical Theory of Networks and Systems, ISBN 978-1-5323-1358-5, (2016), S. 652-659

http://hdl.handle.net/11299/181518
Braun, Philipp; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl
Model predictive control of residential energy systems using energy storage and controllable loads. - In: Progress in Industrial Mathematics at ECMI 2014, (2016), S. 617-623

https://doi.org/10.1007/978-3-319-23413-7_85
Braun, Philipp; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl
A distributed optimization algorithm for the predictive control of smart grids. - In: IEEE transactions on automatic control, ISSN 1558-2523, Bd. 61 (2016), 12, S. 3898-3911

https://doi.org/10.1109/TAC.2016.2525808
Worthmann, Karl; Proch, Michael; Braun, Philipp; Schlüchtermann, Jörg; Pannek, Jürgen
Towards dynamic contract extension in supplier development. - In: Logistics research, ISSN 1865-0368, Bd. 9.2016, Article 14, insg. 12 Seiten

We consider supplier development within a supply chain consisting of a single manufacturer and a single supplier. Because investments in supplier development are usually relationship-specific, safeguard mechanisms against the hazards of partner opportunism have to be installed. Here, formal contracts are considered as the primary measure to safeguard investments. However, formal contracts entail certain risks, e.g., a lack of flexibility, particular in an ambiguous environment. We propose a receding horizon control scheme to mitigate possible contractual drawbacks while significantly enhancing the supplier development process and, thus, to increase the overall supply chain profit. Our findings are validated by a numerical case study.



http://hdl.handle.net/10419/157739
Worthmann, Karl; Mehrez, Mohamed W.; Zanon, Mario; Mann, George K. I.; Gosine, Raymond G.; Diehl, Moritz
Model predictive control of nonholonomic mobile robots without stabilizing constraints and costs. - In: IEEE transactions on control systems technology, ISSN 1558-0865, Bd. 24 (2016), 4, S. 1394-1406

http://dx.doi.org/10.1109/TCST.2015.2488589
Worthmann, Karl; Braun, Philipp; Proch, Michael; Schlüchtermann, Jörg; Pannek, Jürgen
On contractual periods in supplier development. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 49 (2016), 2, S. 60-65

http://dx.doi.org/10.1016/j.ifacol.2016.03.011
Braun, Philipp; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl
Predictive control of a smart grid: a distributed optimization algorithm with centralized performance properties. - In: 2015 54th IEEE Conference on Decision and Control (CDC), ISBN 978-1-4799-7886-1, (2015), S. 5593-5598

http://dx.doi.org/10.1109/CDC.2015.7403096
Worthmann, Karl; Mehrez, Mohamed W.; Zanon, Mario; Mann, George K. I.; Gosine, Raymond G.; Diehl, Moritz
Regulation of differential drive robots using continuous time MPC without stabilizing constraints or costs. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 48 (2015), 23, S. 129-135

http://dx.doi.org/10.1016/j.ifacol.2015.11.272
Braun, Philipp; Grüne, Lars; Kellett, Christopher M.; Weller, Steven R.; Worthmann, Karl
A real-time pricing scheme for residential energy systems using a market maker. - In: Proceedings of 2015 Australian Control Conference (AUCC 2015), ISBN 978-1-922107-69-5, (2015), S. 259-262

http://ieeexplore.ieee.org/xpl/articleDetails.jsp?arnumber=7361944
Worthmann, Karl; Reble, Marcus; Grüne, Lars; Allgöwer, Frank
Unconstrained nonlinear MPC: performance estimates for sampled-data systems with zero order hold. - In: 2015 54th IEEE Conference on Decision and Control (CDC), ISBN 978-1-4799-7886-1, (2015), S. 4971-4976

http://dx.doi.org/10.1109/CDC.2015.7402996
Worthmann, Karl; Kellett, Christopher M.; Braun, Philipp; Grüne, Lars; Weller, Steven R.
Distributed and decentralized control of residential energy systems incorporating battery storage. - In: IEEE transactions on smart grid, Bd. 6 (2015), 4, S. 1914-1923

http://dx.doi.org/10.1109/TSG.2015.2392081
Worthmann, Karl; Kellett, Christopher M.; Grüne, Lars; Weller, Steven R.
Distributed control of residential energy systems using a market maker. - In: IFAC Proceedings Volumes, ISSN 1474-6670, Bd. 47 (2014), 3, S. 11641-11646

https://doi.org/10.3182/20140824-6-ZA-1003.01785
Boccia, Andrea; Grüne, Lars; Worthmann, Karl
Stability and feasibility of state-constrained linear MPC without stabilizing terminal constraints. - In: MTNS 2014, ISBN 978-90-367-6321-9, 2014, Paper TuA07.4, insges. 8 S.

Worthmann, Karl; Reble, Marcus; Grüne, Lars; Allgöwer, Frank
Nonlinear MPC: the impact of sampling on closed loop stability. - In: Proceedings in applied mathematics and mechanics, ISSN 1617-7061, Bd. 14 (2014), 1, S. 911-912

http://dx.doi.org/10.1002/pamm.201410436
Boccia, Andrea; Grüne, Lars; Grüne, Lars *1967-*;
Stability and feasibility of state constrained MPC without stabilizing terminal constraints. - In: Systems & control letters, ISSN 1872-7956, Bd. 72 (2014), S. 14-21

http://dx.doi.org/10.1016/j.sysconle.2014.08.002
Worthmann, Karl; Damm, Tobias; Grüne, Lars; Stieler, Marleen
An exponential turnpike theorem for dissipative discrete time optimal control problems. - In: SIAM journal on control and optimization, ISSN 1095-7138, Bd. 52 (2014), 3, S. 1935-1957

http://dx.doi.org/10.1137/120888934
Worthmann, Karl; Reble, Marcus; Grüne, Lars; Allgöwer, Frank
The role of sampling for stability and performance in unconstrained nonlinear model predictive control. - In: SIAM journal on control and optimization, ISSN 1095-7138, Bd. 52 (2014), 1, S. 581-605

http://dx.doi.org/10.1137/12086652X
Grüne, Lars; Allgöwer, Frank; Findeisen, Rolf; Fischer, Jörg; Groß, Dominik; Hanebeck, Uwe D.; Kern, Benjamin; Müller, Matthias A.; Pannek, Jürgen; Reble, Marcus
Distributed and networked model predictive control. - In: Control theory of digitally networked dynamic systems, (2014), S. 111-167