On extremum seeking controllers based on the Lie bracket approximation in domains with obstacles

作     者：Victoria Grushkovskaya Alexander Zuyev Christian Ebenbauer 

作者机构：Institute for Systems Theory and Automatic Control University of Stuttgart Germany Institute of Applied Mathematics & Mechanics National Academy of Sciences of Ukraine Max Planck Institute for Dynamics of Complex Technical Systems Magdeburg Germany 

出 版 物：《PAMM》 

年 卷 期：2018年第18卷第1期

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

摘      要：In this paper, we consider the problem of extremum seeking in the presence of obstacles. The analytical expression of the cost function as well as locations and shapes of the obstacles are assumed to be partially or completely unknown. We describe a broad family of control algorithms for a unicycle type system, which provides a solution of the above problem based on Lie bracket approximation ideas. The obtained controllers generalize some known results and allow to construct new control strategies. Furthermore, it is shown that gradient-free control algorithms can be used for excluding the attraction of trajectories to undesirable equilibriuma in obstacle avoidance problems.