Search arXiv⌕ Search

arXiv subjects

Matthias A. Müller

Publications and source records attributed to Matthias A. Müller.

113 records · Page 7Linked to original sources
arXiv2020

Online Gradient Descent for Linear Dynamical Systems

In this paper, online convex optimization is applied to the problem of controlling linear dynamical systems. An algorithm similar to online gradient descent, which can handle time-varying and unknown cost functions, is proposed. Then, performance guarantees are derived in terms of regret analysis. We show that the proposed control scheme achieves sublinear regret if the variation of the cost functions is sublinear. In addition, as a special case, the system converges to the optimal equilibrium if the cost functions are invariant after some finite time. Finally, the performance of the resulting closed loop is illustrated by numerical simulations.

math.OC↗
arXiv2020

Linear robust adaptive model predictive control: Computational complexity and conservatism -- extended version

In this paper, we present a robust adaptive model predictive control (MPC) scheme for linear systems subject to parametric uncertainty and additive disturbances. The proposed approach provides a computationally efficient formulation with theoretical guarantees (constraint satisfaction and stability), while allowing for reduced conservatism and improved performance due to online parameter adaptation. A moving window parameter set identification is used to compute a fixed complexity parameter set based on past data. Robust constraint satisfaction is achieved by using a computationally efficient tube based robust MPC method. The predicted cost function is based on a least mean squares point estimate, which ensures finite-gain $\mathcal{L}_2$ stability of the closed loop. The overall algorithm has a fixed (user specified) computational complexity. We illustrate the applicability of the approach and the trade-off between conservatism and computational complexity using a numerical example. This paper is an extended version of~[1], and contains additional details regarding the theoretical proof of Theorem~1, the numerical example, and the offline computations in Appendix~A--B.

eess.SY↗
arXiv2020

A nonlinear model predictive control framework using reference generic terminal ingredients -- extended version

In this paper, we present a quasi infinite horizon nonlinear model predictive control (MPC) scheme for tracking of generic reference trajectories. This scheme is applicable to nonlinear systems, which are locally incrementally stabilizable. For such systems, we provide a reference generic offline procedure to compute an incrementally stabilizing feedback with a continuously parameterized quadratic quasi infinite horizon terminal cost. As a result we get a nonlinear reference tracking MPC scheme with a valid terminal cost for general reachable reference trajectories without increasing the online computational complexity. As a corollary, the terminal cost can also be used to design nonlinear MPC schemes that reliably operate under online changing conditions, including unreachable reference signals. The practicality of this approach is demonstrated with a benchmark example. This paper is an extended version of the accepted paper [1], and contains additional details regarding \textit{robust} trajectory tracking (App.~B), continuous-time dynamics (App.~C), output tracking stage costs (App.~D) and the connection to incremental system properties (App.~A).

eess.SY↗
arXiv2019

Economic MPC using a Cyclic Horizon with Application to Networked Control Systems

In this paper, we analyze an economic model predictive control scheme with terminal region and cost, where the system is optimally operated in a certain subset of the state space. The predictive controller operates with a cyclic horizon, which means that starting from an initial length, the horizon is reduced by one at each time step before it is restored to its maximum length again after one cycle. We give performance guarantees for the closed loop, and under a suitable dissipativity condition, establish convergence to the optimal subset. Moreover, we present conditions under which asymptotic stability of the optimal subset can be guaranteed. The results are illustrated in a practical example from the context of Networked Control Systems, which initially motivated the development of the theory presented in this paper.

eess.SY↗