Having access to the internal state of a dynamical system is of crucial importance for many control applications. In most practical cases, however, the state cannot be completely measured due to physical or economic reasons, demanding the use of appropriate reconstruction methods that solely rely on the available measurement data and the system description. This represents a challenging problem of high practical relevance, particularly in the presence of nonlinear systems and when robustness to model errors and measurement noise must be ensured. For this purpose, modern optimization-based state estimation strategies such as moving horizon estimation (MHE) are particularly suitable.
In this talk, we present various recent results in the field of nonlinear MHE theory. We show how desired robust stability guarantees can be given under realistic conditions by using a Lyapunov function approach and provide suitable methods to verify the underlying nonlinear detectability property. Furthermore, we discuss extensions for real-time capability of MHE, joint state and parameter estimation (particularly robust against weak excitation), as well as Gaussian-process based and event-triggered MHE. Moreover, we draw connections to optimal control and turnpikes, leading to a new perspective on optimization-based state estimation and ultimately to novel performance estimates and regret guarantees for MHE. Finally, we discuss applications of the developed theory to the training of neural networks, which can be viewed as solving complex batch estimation problems. This allows us to quantify the performance of the training algorithm and to derive novel bounds on the regret with respect to a challenging benchmark solution.
Matthias A. Müller received a Diploma degree in engineering cybernetics from the University
of Stuttgart, Germany, an M.Sc. in electrical and computer engineering from the University of
Illinois at Urbana-Champaign (both in 2009), and a Ph.D. in mechanical engineering from the University of Stuttgart in 2014. Since 2019, he is Director of the Institute of Automatic Control and Full Professor at the Leibniz University Hannover, Germany. His research interests include nonlinear control and estimation, model predictive control, and data- and learning-based control, with application in different fields including biomedical engineering and robotics. He has received various awards for his work, including the European Systems & Control PhD Thesis Award, an ERC Starting Grant from the European Research Council, the IEEE CSS George S. Axelby Outstanding Paper Award, the Brockett-Willems Outstanding Paper Award, and the Journal of Process Control Paper Award. He serves/d as an associate editor for Automatica and as an editor of the International Journal of Robust and Nonlinear Control.
