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
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
Idempotent relations, semi-projections, and generalized inverses. - In: Contributions to mathematics and statistics, (2021), S. 87-110
PT-symmetric Hamiltonians as couplings of dual pairs. - In: Contributions to mathematics and statistics, (2021), S. 55-68
Twenty years of continuous multiobjective optimization in the twenty-first century. - In: EURO journal on computational optimization, ISSN 2192-4414, Bd. 9 (2021), 100014, insges. 15 S.
The survey highlights some of the research topics which have attracted attention in the last two decades within the area of mathematical optimization of multiple objective functions. We give insights into topics where a huge progress can be seen within the last years. We give short introductions to the specific sub-fields as well as some selected references for further reading. Primarily, the survey covers the progress in the development of algorithms. In particular, we discuss publicly available solvers and approaches for new problem classes such as non-convex and mixed integer problems. Moreover, bilevel optimization problems and the handling of uncertainties by robust approaches and their relation to set optimization are presented. In addition, we discuss why numerical approaches which do not use scalarization techniques are of interest.
https://doi.org/10.1016/j.ejco.2021.100014
Balanced truncation model reduction for symmetric second order systems - a passivity-based approach. - In: SIAM journal on matrix analysis and applications, ISSN 1095-7162, Bd. 42 (2021), 4, S. 1602-1635
We introduce a model reduction approach for linear time-invariant second order systems based on positive real balanced truncation. Our method guarantees to preserve asymptotic stability and passivity of the reduced order model as well as the positive definiteness of the mass and stiffness matrices. Moreover, we receive an a priori gap metric error bound. Finally we show that our method based on positive real balanced truncation preserves the structure of overdamped second order systems.
https://doi.org/10.1137/20M1346109
Hamiltonicity of random subgraphs of the hypercube. - In: Proceedings of the Thirty-Second Annual ACM-SIAM Symposium on Discrete Algorithms, (2021), S. 889-898
https://dl.acm.org/doi/10.5555/3458064.3458120
Predictive path following control without terminal constraints. - In: Recent advances in model predictive control, (2021), S. 1-26
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
Some notes on port-Hamiltonian systems on Banach spaces. - In: IFAC-PapersOnLine, ISSN 2405-8963, Bd. 54 (2021), 19, S. 223-229
We consider port-Hamiltonian systems from a functional analytic perspective. Dirac structures and Hamiltonians on Banach spaces are introduced, and an energy balance is proven. Further, we consider port-Hamiltonian systems on Banach manifolds, and we present some physical examples that fit into the presented theory.
https://doi.org/10.1016/j.ifacol.2021.11.082