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Polynomial Approximation for Data-Driven System Analysis and Control of Nonlinear Systems

Medium: Buch
ISBN: 978-3-8325-5886-4
Verlag: Logos
Erscheinungstermin: 15.12.2024
Lieferfrist: bis zu 10 Tage

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.


Produkteigenschaften


  • Artikelnummer: 9783832558864
  • Medium: Buch
  • ISBN: 978-3-8325-5886-4
  • Verlag: Logos
  • Erscheinungstermin: 15.12.2024
  • Sprache(n): Englisch
  • Auflage: Erscheinungsjahr 2024
  • Produktform: Kartoniert, PB
  • Seiten: 193
  • Format (B x H): 145 x 210 mm
  • Ausgabetyp: Kein, Unbekannt

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