Polynomial Approximation For Data Driven System Analysis And Control Of Nonlinear Systems
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Polynomial Approximation for Data-Driven System Analysis and Control of Nonlinear Systems
Author: Tim Martin
language: en
Publisher: Logos Verlag Berlin GmbH
Release Date: 2024-12-15
This thesis presents data-driven methods for nonlinear systems, enabling the verification of system-theoretical properties and the design of state feedbacks based on measured trajectories. Despite noisy data, the developed methods provide rigorous guarantees and leverage convex optimization. Classical control techniques require a mathematical model of the system dynamics, which derivation from first principles often demands expert knowledge or is time-consuming. In contrast, data-based control methods determine system properties and controllers from system trajectories. Whereas recent developments address linear systems, dynamical systems are generally nonlinear in practice. Therefore, this thesis first introduces a data-based system representation for unknown polynomial systems to determine dissipativity and integral quadratic constraints via sum-of-squares optimization. The second part of the thesis establishes a polynomial representation of nonlinear systems based on polynomial interpolation. Due to the unknown interpolation polynomial, a set of polynomials containing the actual interpolation polynomial is deduced from noisy data. This set, along with a polynomial bound on the approximation error, forms the basis for determining dissipativity properties and designing state feedbacks with stability guarantees utilizing robust control techniques and sum-of-squares relaxation.
Hybrid and Networked Dynamical Systems
Hybrid and Networked Dynamical Systems treats a class of systems that is ubiquitous in everyday life. From energy grids to fleets of robots or vehicles to social networks to biological networks, the same scenario arises: dynamical units interact locally through a connection graph to achieve a global task. The book shows how analysis and design tools can be adapted for control applications that combine the effects of network-induced interactions and hybrid dynamics with complex results. Following a scene-setting introduction, the remaining 12 chapters of the book are divided into three parts and provide a unique opportunity to describe the big picture that is the culmination of years of recent research activity. The contributing authors expand on their ideas at greater length than is possible in an archival research paper and use in-depth examples to illustrate their theoretical work. The widespread importance of hybrid and networked systems means that the book is of significant interest to academic researchers working in applied mathematics, control, and electrical, mechanical and chemical engineering and to their industrial counterparts.
Analysis and design of aperiodic sampling in control systems
Author: Stefan Wildhagen
language: en
Publisher: Logos Verlag Berlin GmbH
Release Date: 2023-11-02
This thesis addresses data-driven analysis as well as prediction-based design of aperiodic sampling in control systems. In many modern control applications, the traditional view of sampling and controlling in a periodic fashion must be abandoned due to varying transmission delays, data loss or uneven computational latencies. The effect of these undesired aperiodicities on the closed loop must thus be analyzed. In addition, a targeted aperiodic design of the sampling pattern, e.g. via event-triggered control (ETC), often allows for a better usage of bandwidth than periodic concepts. We consider both perspectives in this thesis. In particular, first we provide methods to analyze stability of control systems under arbitrary aperiodic sampling directly from recorded data. Previous approaches to this end required model knowledge, which might be challenging to obtain. Second, we propose a prediction-based approach for design of the aperiodic sampling pattern, called rollout ETC. This approach allows for predictability of the required communication resources and a guarantee of improved sample efficiency, which were both difficult to address in existing ETC schemes.