A Hybrid Systems Approach for Distributed Nonsmooth Optimization in Asynchronous Multi-Agent Sampled-Data Systems*

We study the problem of robust distributed nonsmooth optimization in a network of sampled data systems with separable response maps but coupled dynamics. Each agent of the network is assumed to have an individual clock and an individual nonsmooth output function, as well as set-valued internal dynamics that are coupled with the internal dynamics of its neighboring agents. In order to achieve robust convergence and stability of the optimal point of the response map of the entire network, we design a distributed deterministic model-free logic-based hybrid controller that globally and robustly synchronizes the clocks of the sampled data systems, while at the same time optimizes the response map of every agent by using only sampled measurements of their individual outputs. We present numerical simulations illustrating the results.