Verification Of System Properties Of Polynomial Systems Using Discrete Time Approximations And Set Based Analysis

Verification of System Properties of Polynomial Systems Using Discrete-time Approximations and Set-based Analysis

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.

Automated Technology for Verification and Analysis

This book constitutes the refereed proceedings of the Third International Symposium on Automated Technology for Verification and Analysis, ATVA 2006, held in Beijing, China in October 2006. The 35 revised full papers presented together with abstracts of three keynote papers were carefully reviewed and selected from 137 submissions.