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Extremum seeking control of nonlinear dynamic systems using Lie bracket approximations
Author(s) -
Grushkovskaya Victoria,
Ebenbauer Christian
Publication year - 2021
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.3152
Subject(s) - nonlinear system , control theory (sociology) , singular perturbation , mathematics , exponential stability , perturbation (astronomy) , lie group , nonlinear control , stability (learning theory) , lyapunov function , lyapunov stability , lie algebra , optimal control , stability theory , control (management) , mathematical optimization , computer science , mathematical analysis , artificial intelligence , pure mathematics , physics , quantum mechanics , machine learning
Summary In this article, we consider extremum seeking problems for a general class of nonlinear dynamic control systems. The main result of the article is a broad family of control laws which optimize the steady‐state performance of the system. We prove practical asymptotic stability of the optimal steady‐state and, moreover, propose sufficient conditions for the asymptotic stability in the sense of Lyapunov. The results generalize and extend existing results which are based on Lie bracket approximations. In particular, our approach does not rely on singular perturbation theory, as commonly used in extremum seeking of nonlinear dynamic systems.