Stabilizability of Nash Equilibrium for Game-Based Control Systems

Abstract. We investigate the stabilizability of Nash equilibrium for a general class of the nonlinear game-based control system (GBCS), which was initially introduced to model the control systems with strategic behavior, such as social, economic, and “intelligent” systems. The GBCS exhibits a hierarchical structure comprising a higher-level regulator and multiple lower-level rational agents. The regulator functions as the global controller and makes decisions first, after which the agents attempt to optimize their respective objective functions. For a given control of the regulator, the lower-level agents engage in a noncooperative game. The stabilizability problem addresses whether the regulator can stabilize the system by regulating the Nash equilibrium established by the agents at the lower level. In this paper, we will first formulate the stabilizability problem of the general nonlinear GBCS. Some explicit necessary and/or sufficient algebraic conditions on the stabilizability of Nash equilibrium are given by investigating the solvability relationship between the associated Hamilton–Jacobi–Isaacs equations and the algebraic Riccati equations related to an approximated linear-quadratic GBCS.