Distributed Strategy Design for Autonomous Multi-Cluster Games With High-Order Nonlinear Physical Players and Its Application to Clustered Electricity Markets

This paper considers the distributed autonomous multi-cluster games (MCGs) of physical players. In contrast to existing MCGs, the players in our MCG have high-order nonlinear dynamics. Moreover, these players are restricted by three kinds of constraints: local inequality constraints, intra-cluster and inter-cluster coupling inequality constraints. As far as we know, constrained MCGs with high-order nonlinear players have not been investigated. Existing distributed game strategies cannot handle our problem, mainly owing to the simultaneous presence of inequality constraints and high-order nonlinear dynamics. We exploit a distributed strategy, and give its performance analysis rigorously. With our strategy, those heterogeneous high-order nonlinear physical players do carry out MCG tasks autonomously. Also, the exact variational generalized Nash equilibrium (vGNE) of our MCG is sough via the strategy, even if the dynamics contains unknown parameters. Finally, the application of our method to clustered electricity market games (EMGs) is presented. Under our method, boiler-turbine generation systems (BTGSs) take part in clustered EMGs zealously and spontaneously, without the assistance of human beings. Note to Practitioners—The intellectualization of cyber-physical systems (CPSs) stimulates physical systems to execute distributed game tasks autonomously, e.g., the autonomous electricity market games of generators and the autonomous attack-defense games of unmanned aerial vehicles (UAVs). However, many existing works on games with physical systems do not involve constraints, and only consider first- or second-order (linear) dynamics. Besides, most existing methods cannot seek the exact GNE under the simultaneous appearance of constraints and system dynamics. Here our problem involves more complicated dynamics and constraints of players, which covers existing related problems. Moreover, under our method, complicated high-order nonlinear physical players can autonomously perform constrained games tasks, promoting the intellectualization of CPSs.