Saddle-Flow Dynamics for Distributed Feedback-Based Optimization

Abstract

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.