# Manuel Schallar's talk on Structure-exploiting optimal control of port-Hamiltonian systems and Karl Worthmann's talk on Model predictive control for systems with null-controllable homogeneous approximation

We have a double-bill.

**Time, Date, Location**: 11:00, Friday, 9 January, 2023, Brian Anderson Building Seminar Room

The details are given below.

**Title:** Structure-exploiting optimal control of port-Hamiltonian systems

**Abstract:** We consider optimal control of port-Hamiltonian systems by minimizing
the energy supplied via the ports. Albeit this intrinsic choice of the
cost functional, the resulting optimal control problem can be singular,
i.e., it is in general not coercive in the control variable. However to
the dissipative structure of port-Hamiltonian systems and the strong
intertwinement of cost and dynamics, we show under suitable assumptions
that, despite this singularity, optimal controls exist, can be
characterized by optimality conditions and exhibit a particular
stability behavior towards a conservative subspace.

**Title:** Model predictive control for systems with null-controllable homogeneous approximation

**Abstract:** The stabilization of non-holonomic mobile robots is challenging
according to A. Astolfi, see [1]. In particular, it was shown in [2]
that the set-point stabilization cannot be achieved using MPC based on
quadratic costs without stabilizing terminal conditions. A remedy is the
use of tailored stage or terminal costs, see, e.g. [3]. In the first
part of the talk, we recap these findings. Then, we present the
framework proposed in [4], which allows to systematically design stage
costs such that local asymptotic stability of the origin w.r.t. the MPC
closed loop is ensured for a system class including the mobile-robot
example. To this end, we show that cost controllability, a sufficient
stability condition, holds making use of the homogeneous approximation.

- [1] A. Astolfi: Discontinuous control of nonholonomic systems. Systems & Control Letters 27(1): 37-45, 1996.
- [2] M.A. Müller, K. Worthmann: Quadratic costs do not always work in MPC. Automatica 82: 69-277, 2017.
- [3] K. Worthmann, M.W. Mehrez, M. Zanon, G.K.I. Mann, R.G. Gosine, M. Diehl: Model predictive control of nonholonomic mobile robots without stabilizing constraints and costs. IEEE Transactions on Control Systems Technology 24(4):1394-1406, 2016.
- [4] J.-M. Coron, L. Grüne, K. Worthmann: Model Predictive Control, Cost Controllability, and Homogeneity. SIAM Journal on Control and Optimization 58(5):2979-2996, 2020.

**Bios:** Manuel Schaller obtained a M.Sc. in Mathematics in 2017 from the
University of Bayreuth with focus on PDE-constrained optimization and
numerics. In 2021, he received a PhD in Applied Mathematics at the
University of Bayreuth under the joint supervision of Prof. Lars Grüne
and Prof. Anton Schiela. During this time, his research was focused on
stability and sensitivity analysis of (infinite-dimensional) optimal
control problems, in particular turnpike theory and efficient space-time
finite element discretizations for Model Predictive Control.

Currently, Manuel is with the Optimization-based Control Group at Technische Universität Ilmenau, where he holds a position as Lecturer. In his research, he focusses on singular optimal control of port-Hamiltonian systems and guarantees for data-based surrogate models for control systems with particular applications in retinal laser treatment and adaptive high-rise buildings.

In 2020, he was appointed as GAMM (German Association of Applied Mathematics and Mechanics) Junior fellow.

Karl Worthmann received his Ph.D. degree in mathematics from the University of Bayreuth, Germany, in 2012. 2014 he was appointed assistant professor for ‘‘Differential Equations’’ at Technische Universität Ilmenau (TU Ilmenau), Germany. 2019 he was promoted to full professor after receiving the Heisenberg-professorship ‘‘Optimization-based Control’’ by the German Research Foundation in 2018. He was recipient of the Ph.D. Award from the City of Bayreuth, Germany, and stipend of the German National Academic Foundation. 2013 he has been appointed Junior Fellow of the Society of Applied Mathematics and Mechanics (GAMM), where he served as speaker in 2014 and 2015. Currently, Karl Worthmann is chairman “Mathematical Systems Theory” of the interdisciplinary GAMM activity group “Dynamics and Control Theory” and recently served as programme co-chair for the MTNS 2022. Karl Worthmann’s current research interests include systems and control theory with a particular focus on nonlinear model predictive control, stability analysis, and data-driven control.