Polynomial Approximation for Data-Driven System Analysis and Control of Nonlinear Systems
Produktnummer:
180d34e86505434b31966d860b40efce15
Autor: | Martin, Tim |
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Themengebiete: | Dissipativity Robust Control Sum-of-Squares Optimization System Identification |
Veröffentlichungsdatum: | 15.12.2024 |
EAN: | 9783832558864 |
Sprache: | Englisch |
Seitenzahl: | 193 |
Produktart: | Kartoniert / Broschiert |
Verlag: | Logos Berlin |
Produktinformationen "Polynomial Approximation for Data-Driven System Analysis and Control of Nonlinear Systems"
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.

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