Stackelberg Game Theory-Based Optimization of High-Order Robust Control for Fuzzy Dynamical Systems

A novel class of high-order robust controls is presented for uncertain fuzzy systems in this article. The optimal tunable parameters are also obtained based on the Stackelberg game theory. First, a dynamical system structure is formulated with uncertainty. The uncertain portion in the system is bounded, nonlinear, and time-varying which is within prescribed fuzzy set. Thus, this is a fuzzy system. Then, the proof based on the Lyapunov minimax approach shows that the novel high-order robust controls are able to assure deterministic system performance, which is uniform boundedness and ultimate uniform boundedness. Furthermore, the optimal choice of the tunable parameters in the control is considered. We creatively apply the Stackelberg strategy to solving the optimization problem. Two parameters are regarded as leader and follower in a sequential game, respectively. Based on the Stackelberg game rules, we are able to design different cost functions for different parameters. The cost functions include both performance measures and control cost. Finally, the simulations of an electronic throttle system are presented for demonstration.