Distributed Extremum Seeking in Multi-Agent Systems with Arbitrary Switching Graphs

This paper studies the problem of averaging-based extremum seeking in dynamical multi-agent systems with time-varying communication graphs. We consider a distributed consensus-optimization problem where the plants and the controllers of the agents share information via time-varying graphs, and where the cost function to be minimized corresponds to the summation of the individual response maps generated by the agents. Although the problem of averaging-based extremum seeking control in multi-agent dynamical systems with timeinvariant graphs has been extensively studied, the case where the graph is time-varying remains unexplored. In this paper we address this problem by making use of recent results for generalized set-valued hybrid extremum seeking controllers, and the framework of switched differential inclusions and common Lyapunov functions. For the particular consensus-optimization problem considered in this paper, a semi-global practical stability result is established. A numerical example in the context of dynamic electricity markets illustrates the results.