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

By (author) Tim Martin

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Extent: 193 pages

Publisher: Logos Verlag Berlin

Subjects: Technical Sciences: Computer Science, Engineering, IT, & Math

Language: English

Paperback (Published)

(December 2024)

ISBN: 9783832558864

5.71 x 8.27 inches

Price: $67.00

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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.

  • By (author) Tim Martin

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