A novel single fuzzy approximation based adaptive control for a class of uncertain strict-feedback discrete-time nonlinear systems

This paper investigates the problem of adaptive fuzzy control for a class of uncertain nonlinear strict-feedback discrete-time systems with unknown system functions and control gain functions. Following the idea of single neural network (SNN) approximation, single fuzzy logic system(SFLS) approximation is first proposed and synthesized with “minimal learning parameter (MLP)” technique into a novel adaptive fuzzy control design methodology for the concerned systems. With the help of the MLP technique, the problem of “curse of dimension” is circumvented, and the adaptive mechanism with minimal learning parameterization is achieved. Meanwhile, by employing the SFLC approximation in the adaptive control synthesis, all unknown functions at the intermediate steps are passed down in the controller design process, and only one fuzzy logic system (FLS) is employed to deal with the lumped unknown functions at the last step. Following this approach, the problem of “explosion of complexity” inherent in backstepping method is also avoided, and the designed controllers contain only one actual control law and one adaptive law. Thereby, the number of parameters updated online for the entire discrete-time system is reduced to only one. As a result, the controller is much simpler, the computational burden is much lighter and the learning time tends to much shorter. The closed-loop stability in the sense of semi-globally uniformly ultimately bounded (SGUUB) can be guaranteed via Lyapunov theory. Finally, simulation results via two examples are given to illustrate the performance of the proposed scheme.