Extremum Seeking and Adaptive Dynamic Programming for Distributed Feedback Optimization

This paper studies the distributed feedback optimization problem for linear multi-agent systems without precise knowledge of local costs and agent dynamics. The proposed solution is based on a hierarchical approach that uses upper-level coordinators to adjust reference signals toward the global optimum and lower-level controllers to regulate agents' outputs toward the reference signals. In the absence of precise information on local gradients and agent dynamics, an extremum-seeking mechanism is used to enforce a gradient descent optimization strategy, and an adaptive dynamic programming approach is taken to synthesize an internal-model-based optimal tracking controller. The whole procedure relies only on measurements of local costs and input-state data along agents' trajectories. Moreover, under appropriate conditions, the closed-loop signals are bounded and the output of the agents exponentially converges to a small neighborhood of the desired extremum. A numerical example is conducted to validate the efficacy of the proposed method.