Distributed Generalized Nash Equilibrium Seeking for Linear Systems Over a Switching Network

This article concerns distributed generalized Nash equilibrium (GNE) seeking in an N-player game with linear dynamics over a jointly strongly connected switching network. The main challenge of this problem is the design of appropriate updating laws that ensure convergence under a jointly strongly connected switching network. Such a design must also respect inequality constraints and address the complexity of linear dynamics. Projection-based pseudo-gradient method is proposed to seek the GNE while satisfying both the individual and the shared inequality constraints. Furthermore, the jointly strongly connected switching network, which may be disconnected at any time instant, entails resorting to the generalized Barbalat’s lemma in the convergence analysis. We also discuss an application to doubly fed induction generators (DFIGs) subject to total power limitations and individual power ranges, providing simulation results to verify the proposed algorithm.