Stabilizability of Game-Based Control Systems
Renren Zhang · 2023
We investigate the stabilizability of Nash equilibrium of the nonlinear game-based control system (GBCS), which has a similar decision-making structure as Stackelberg Games: one leader and multiple rational followers or agents. While the leader of the GBCS is a macro-regulator rather than a game player. The stabilizability problem is that whether the regulator can stabilize the system by regulating the Nash equilibrium formed by the agents at the lower level. The stabilizability of linear-quadratic GBCS has been investigated in [10]. In this paper, we will first formulate the stabilizability problem of the general nonlinear GBCS. Then the stabilizability relationships between the linear-quadratic and nonlinear GBCSs are given, by investigating the solvable relationship of the associated algebraic Riccati equations and nonlinear Hamilton-Jacobi equations.