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A Design of Stable Adaptive Composite Control Systems

In this paper, a stable adaptive composite control system consisting of a PID and a fuzzy controllers is designed to control nonlinear systems. In the fuzzy controller, parameters of membership functions characterizing the linguistic terms change according to some adaptive law. Also, parameters of PID controller change according to some adaptive law. These adaptive laws are based on the Lyapunov synthesis approach. Then, it is proved that the closed-loop system using such an adaptive composite control system is globally stable in the sense that all signals involved are bounded and the tracking error converges to zero. We apply this adaptive composite control system to control a nonlinear system.