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Approach of adaptive control for a class of nonlinear systems using fuzzy approximator

Based on the Lyapunov synthesis approach and regarding the fuzzy system as approximator to approximate unknown functions in the system to be controlled, several adaptive control schemes have been developed during the last decade or more. Actually, (i) most of them just consider SISO systems (which can avoid the challenge of the coupling between control inputs); (ii) the system state have been involved in the fuzzy controller directly (in this way, there is no need to consider the problem of state observer). This paper develops a design methodology for a class of MIMO nonlinear systems with state observer. The overall adaptive scheme is shown to guarantee the tracking error, between the outputs of system and the desired values, to be asymptotical in decay, while maintaining all singles involved stable and forcing the estimated state to follow the real state rapidly.