Adaptive fuzzy robust control of a class of nonlinear systems via small gain theorem

This paper presents a novel adaptive fuzzy robust control (AFRC) algorithm for a class of nonlinear systems with partly linearly parameterized system models, unknown system nonlinearities and external unknown disturbances. For linearly parameterized system models, discontinuous-projection-based adaptive control law is used to estimate system parameters. The Takagi-Sugeno fuzzy logic systems are used to approximate unknown system nonlinearities. Robust control law ensures the robustness of closed-loop control system. This proposed AFRC effectively combines techniques of adaptive control and fuzzy control and it improves control performance by retaining the advantages of both. A systematic design procedure of AFRC is developed by combining the backstepping technique and small-gain approach. The closed-loop stability is studied using small gain theorem and the control system is proved to be semi-globally uniformly ultimately bounded.