Robust adaptive fuzzy sliding mode control for a class of perturbed strict-feedback nonlinear systems

In this paper, a robust adaptive fuzzy sliding mode controller is proposed to deal with the tracking control problem for a class of single-input single-output (SISO) perturbed strict-feedback nonlinear systems. It is known that the presence of perturbations is a very common problem in various kinds of engineering systems, and these perturbations involve unmodelled dynamics, external disturbances, and parameter variations. First, the unknown parameter vectors of strict-feedback system is on-line learned to compensate their effects. Besides the parameter variations, the upper bounds of these perturbations are often difficult to be obtained. Therefore, fuzzy logic systems and adaptive laws are applied to approximate the unknown upper bounds of the remained perturbations. In addition, the absolute minimum between the upper bound of perturbation and its learning function is updated to enhance the system performance. By introducing Lyapunov stability theorem as well as the theory of sliding mode control, not only the robust stability of the overall system can be ensured, but also good tracking performance can be obtained. Finally, an example of spring-mass-damper nonlinear system in the presence of perturbations confirms the effectiveness and the feasibility of the proposed control.