搜索系统的Lie逼近
Lie Bracket Approximation of Extremum Seeking Systems
摘要：
寻优反馈是将动力系统控制到部分或完全未知映射的极值的一种有效方法。它往往需要先进的系统理论工具来理解极值寻求系统的定性行为。本文介绍了极值搜索的一种新的解释。证明了求极值系统的轨线可以用求极值系统的向量场的某些李括号的轨线来近似。结果表明，李括号系统直接揭示了极值搜索系统的优化行为。进一步证明了李括号系统的一致渐近稳定性蕴含着相应极值搜索系统的一致渐近稳定性.我们使用已建立的结果，以证明局部和半全局的实际一致渐近稳定性的某一映射的极值多智能体极值搜索系统。
英文摘要：
Extremum seeking feedback is a powerful method to steer a dynamical system to an extremum of a partially or completely unknown map. It often requires advanced system-theoretic tools to understand the qualitative behavior of extremum seeking systems. In this paper, a novel interpretation of extremum seeking is introduced. We show that the trajectories of an extremum seeking system can be approximated by the trajectories of a system which involves certain Lie brackets of the vector fields of the extremum seeking system. It turns out that the Lie bracket system directly reveals the optimizing behavior of the extremum seeking system. Furthermore, we establish a theoretical foundation and prove that uniform asymptotic stability of the Lie bracket system implies practical uniform asymptotic stability of the corresponding extremum seeking system. We use the established results in order to prove local and semi-global practical uniform asymptotic stability of the extrema of a certain map for multi-agent extremum seeking systems.
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