Stratified Game-Theoretic Optimization of Robust Control Design for Fuzzy Dynamical Systems: A Hybrid Nash–Stackelberg Strategy

In this article, the uncertain system parameters and disturbances are considered and described by fuzzy sets theory. Then, a new form of robust control is designed for the fuzzy dynamical systems. The system is proved to be uniformly bounded and uniformly ultimately bounded according to Lyapunov approach. To seek a better system performance and lower control cost, an optimization problem with multi parameters is formulated. A two-level game structure is proposed to find the optimal solution. First, the generalized Stackelberg game theory is applied when there are one leader and two followers. Then, the Nash game theory is applied for the two followers. Numerical simulations are performed for verification.