Stable direct adaptive fuzzy control for a class of MIMO non-linear systems

Two new schemes of direct adaptive fuzzy controller for a class of multi-input multi-output non-linear systems with unknown constant gains or function gains are proposed in this paper. The design is based on a modified Lyapunov function and the approximation capability of the first type fuzzy system. The approach is able to avoid the requirement of the upper bound of the first-time derivative of the control gain, which is assumed to know a priori in some of the existing adaptive fuzzy/neural network control schemes. In addition, it is also able to avoid the controller singularity problem. By theoretical analysis, the closed-loop fuzzy control system is proven to be globally stable in the sense that all signals involved are bounded, with tracking errors converging to zero. The simulation results verify the effectiveness the proposed controllers and the theoretical discussion.