Adaptive fuzzy backstepping control for a class of strict-feedback discrete-time nonlinear systems

In this paper, by incorporating "minimal learning parameter (MLP)" technique into an adaptive fuzzy control design framework, a backstepping based control algorithem is presented for a class of uncertain strict-feedback nonlinear discrete-time systems. The proposed scheme is able to circumvent the problem of " curse of dimension" for high-dimensional systems. thus the number of parameters updated online for each subsystem is reduced to one, no matter how many rules are used in fuzzy systems and how many input variables exist in the system. 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.