Sparsity-Constrained Games and Distributed Optimization with Applications to Wide-Area Control of Power Systems.

Multi-agent networked dynamic systems attracted attention of researchers due to their ability to model spatially separated or self-motivated agents. In particular, differential games are often employed to accommodate different optimization objectives of the agents, but their optimal solutions require dense feedback structures, which result in high costs of the underlying communication network. In this work, social linear-quadratic-regulator (LQR) optimization and differential games are developed under a constraint on the number of feedback links among the system nodes. First, a centralized optimization method that employs the Gradient Support Pursuit (GraSP) algorithm and a restricted Newton step was designed. Next, these methods are combined with an iterative gradient descent approach to determine a Nash Equilibrium (NE) of a linear-quadratic game where each player optimizes its own LQR objective under a shared global sparsity constraint. The proposed noncooperative game is solved in a distributed fashion with limited information exchange. Finally, a distributed social optimization method is developed. The proposed algorithms are used to design a sparse wide-area control (WAC) network among the sensors and controllers of a multi-area power system and to allocate the costs of this network among the power companies. The proposed algorithms are analyzed for the Australian 50-bus 4-area power system example.