Gradient-free control algorithms for dynamic optimization problems
According to the materials of scientific report at the meeting of the Presidium of NAS of Ukraine, May 30, 2018
DOI:
https://doi.org/10.15407/visn2018.08.066Keywords:
dynamic optimization problems, extremum seeking, asymptotic stability, gradient-free control algorithms, Lie bracket approximationAbstract
The paper focuses on the study of dynamic optimization problems with cost function, whose analytical expression is partially or completely unknown. This limitation leads to inefficiency of classical control methods, for which the gradient of a cost functions has to be computed explicitly. This paper presents a novel gradient-free control design approach for dynamic optimization problems. It unifies and generalizes some known results and, moreover, allows constructing new controls with favourable properties. In contrast to many existing gradient-free control algorithms which imply only the practical asymptotic stability, we propose conditions for asymptotic (and even exponential) stability in the sense of Lyapunov. The results obtained are illustrated by numerical simulations and experiments with a mobile robot.
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