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
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
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
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
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
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
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
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
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
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