Distributed extremum-seeking control over networks of dynamically coupled unstable dynamic agents

In this paper, a distributed extremum seeking control technique is proposed to solve a class of real-time optimization problems over a network of dynamic agents with unknown unstable dynamics. Each dynamic agent measures a cost that is shared over a network. A dynamic average consensus approach is used to provide each agent with an estimate of the total network cost. The extremum seeking controller operates at each agent to allow each agent to contribute to the optimization of the total cost, in a cooperative fashion. The extremum seeking control technique is based on a proportional-integral approach that provides improvements in transient performance over standard techniques. The contribution of the proposed technique is to solve the simultaneous stabilization and real-time optimization. A dynamic network simulation example is presented to demonstrate the effectiveness of the technique.