Game-Theoretic Feedback-Based Optimization

Abstract

This paper examines the intersection between feedback-based optimization problems and distributed Nash equilibrium seeking algorithms. We consider a modification of typical GNE-seeking problems with affine coupling constraints, wherein each agent's objective additionally depends on the measurable output of a nonlinear input-output mapping. Operator-theoretic methods are leveraged to develop an online distributed algorithm for this class of problems, with convergence criteria provided. We illustrate the algorithm via an application to coordination of distributed energy resources in a power distribution feeder.