A novel adaptive fuzzy control for a class of discrete-time nonlinear systems in strict-feedback form

In this paper, a backstepping based adaptive fuzzy control algorithem is presented for a class of uncertain nonlinear discrete-time systems in the strict-feedback form. By introducing the "minimal learning parameter (MLP)" technique, the proposed scheme is able to circumvent the problem of "curse of dimension" for high-dimensional systems. Meanwhile, all the virtual control laws and actual control law in the system are updated by a novel actual adaptive update law, thus the number of parameters updated online for whole system is only by one. Takagi-Sugeno (T-S) fuzzy systems are used to approximate the unknown system functions. It is shown via Lyapunov theory that all signals in the closed-loop system are semi-globally uniformly ultimately bounded (SGUUB). Finally, a simulation example is employed to illustrate the effectiveness and advantages of the proposed scheme.