Distributed Strategy Design for Multicoalition Games With Autonomous High-Order Players and Its Application in Smart Grids

This article focuses on constrained high-order multicoalition games (MCGs), which differ from most MCGs as they contain the high-order dynamics of players. Furthermore, all players are subject to inequality constraints. Existing distributed strategies for Nash equilibrium (NE) seeking are inapplicable to our problem, due to the presence of high-order dynamics and/or inequality constraints. The coexistence of high-order dynamics and inequality constraints poses significant challenges for distributed strategy design and analysis, since these players’ actions cannot be directly controlled by their inputs while NE must satisfy the constraints. To ensure that the high-order players fulfill the MCG tasks autonomously, we propose a distributed strategy by employing state feedback, gradient descents, and primal–dual methods. Further, we prove the stabilization of high-order players to the NE through our strategy. Additionally, we apply our method to electricity market games (EMGs). Based on our method, boiler–turbine generation systems (BTGSs) can engage in EMGs autonomously, which contributes to enhancing the intellectualization of smart grids.