Distributed Extremum Seeking in Multi-Agent Systems with Arbitrary Switching Graphs * *Research supported in part by AFOSR grant number FA9550-15-1-0155, and NSF grant number ECCS-1508757 (M. Benosman was entirely supported by MERL, without any link to these grants). This work was done in part while J.I. Poveda was an intern at Mitsubishi Electric Research Laboratories, Cambridge, MA, 02139, USA

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 time-invariant 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.