Saddle-Flow Dynamics for Distributed Feedback-Based Optimization

This letter develops a distributed saddle-flow algorithm to regulate the output of a networked system-modeled as static linear map-to the solution of a constrained convex optimization problem. The algorithm is “feedback-based”, in the sense that measurements of the network output are leveraged in the saddle-flow updates to avoid a complete (oracle-based) knowledge of the network map. In the distributed architecture, each actuator has access to only a subset of measurements; nevertheless, supported by a connected communication graph, a distributed protocol is implemented to achieve consensus on pertinent dual variables associated with network-level output constraints and, therefore, on the solution of the constrained problem. Using a LaSalle argument, we show that under an easily satisfiable linear matrix inequality condition the proposed algorithm converges to an optimal primal-dual solution. We demonstrate the effectiveness of the proposed method in a voltage regulation problem for power systems with high penetration of renewable generation.