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arXiv · 1907.02414

Partial Stability Concept in Extremum Seeking Problems

Victoria Grushkovskaya·Alexander Zuyev
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Abstract

The paper deals with the extremum seeking problem for a class of cost functions depending only on a part of state variables of a control system. This problem is related to the concept of partial asymptotic stability and analyzed by Lyapunov's direct method and averaging schemes. Sufficient conditions for the practical partial stability of a system with oscillating inputs are derived with the use of Lie bracket approximation techniques. These conditions are exploited to describe a broad class of extremum-seeking controllers ensuring the partial stability of the set of minima of a cost function. The obtained theoretical results are illustrated by the Brockett integrator and rotating rigid body.

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Victoria Grushkovskaya, Alexander Zuyev. 2019-07-04. Partial Stability Concept in Extremum Seeking Problems. https://doi.org/10.1016/j.ifacol.2019.12.041

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