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Saddle-flow dynamics for distributed feedback-based optimization
C.-Y. Chang, M. Colombino, J. Cortés, E. Dall'Anese
IEEE Control Systems Letters 3 (4) (2019), 948-953

Abstract

This paper 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.

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