Matthias A. Müller

Isabelle Krauss, Victor G. Lopez, Matthias A. Müller

In this paper, we propose a sample-based moving horizon estimation (MHE) scheme for general nonlinear systems to estimate the current system state using irregularly and/or infrequently available measurements. The cost function of the MHE optimization problem is suitably designed to accommodate these irregular output sequences. We also establish that, under a suitable sample-based detectability condition known as sample-based incremental input/output-to-state stability (i-IOSS), the proposed sample-based MHE achieves robust global exponential stability (RGES). Additionally, for the case of linear systems, we draw connections between sample-based observability and sample-based i-IOSS. This demonstrates that previously established conditions for linear systems to be sample-based observable can be utilized to verify or design sampling strategies that satisfy the conditions to guarantee RGES of the sample-based MHE. Finally, the effectiveness of the proposed sample-based MHE is illustrated through a simulation example.

Isabelle Krauss, Victor G. Lopez, Matthias A. Müller

In this paper we propose a detectability condition for nonlinear continuous-time systems with irregular/infrequent output measurements, namely a sample-based version of incremental integral input/output-to-state stability (i-iIOSS). We provide a sufficient condition for an i-iIOSS system to be sample-based i-iIOSS. This condition is also exploited to analyze the relationship between sample-based i-iIOSS and sample-based observability for linear systems, such that previously established sampling strategies for linear systems can be used to guarantee sample-based i-iIOSS. Furthermore, we present a sample-based moving horizon estimation scheme, for which robust stability can be shown. Finally, we illustrate the applicability of the proposed estimation scheme through a biomedical simulation example.

Christian Gatke, Julian D. Schiller, Matthias A. Müller

We provide a detectability analysis for nonlinear large-scale distributed systems in the sense of exponential incremental input/output-to-state stability (i-IOSS). In particular, we prove that the overall system is exponentially i-IOSS if each subsystem is i-IOSS, with interconnections treated as external inputs, and a suitable small-gain condition holds. The analysis is extended to a Lyapunov characterization, resulting in a different quantitative outcome regarding the small-gain condition, which is further analyzed within this work. Moreover, we derive linear matrix inequality conditions posed solely on the local subsystems and their interconnections, which guarantee exponential i-IOSS of the overall distributed system. The results are illustrated on a numerical example.

Victor G. Lopez, Malte Heinrich, Matthias A. Müller

In the reinforcement learning literature, strong theoretical guarantees have been obtained for algorithms applicable to LTI systems. However, in the nonlinear case only weaker results have been obtained for algorithms that mostly rely on the use of function approximation strategies like, for example, neural networks. In this paper, we study the applicability of a known output-feedback Q-learning algorithm to the class of nonlinear systems that admit a Koopman linear embedding. This algorithm uses only input-output data, and no knowledge of either the system model or the Koopman lifting functions is required. Moreover, no function approximation techniques are used, and the same theoretical guarantees as for LTI systems are preserved. Furthermore, we analyze the performance of the algorithm when the Koopman linear embedding is only an approximation of the real nonlinear system. A simulation example verifies the applicability of this method.