Buch, Englisch, 193 Seiten, PB, Format (B × H): 145 mm x 210 mm
ISBN: 978-3-8325-5886-4
Verlag: Logos
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.
Autoren/Hrsg.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
- Technische Wissenschaften Technik Allgemein Technik: Allgemeines
- Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Datenanalyse, Datenverarbeitung
- Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Regelungstechnik
- Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
- Interdisziplinäres Wissenschaften Wissenschaften: Forschung und Information Kybernetik, Systemtheorie, Komplexe Systeme
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung
- Technische Wissenschaften Maschinenbau | Werkstoffkunde Produktionstechnik Fertigungstechnik
