Abstract
A new direct adaptive type-2 fuzzy controller for a nonlinear dynamical system is developed in this paper. The parameters of the membership functions characterizing the linguistic terms in the type-2 fuzzy IF–THEN rules change according to some adaptive law for the purpose of controlling a plant to track a reference trajectory. A supervisory controller is appended to the type-2 fuzzy controller to force the state to be within the constraint set. Stability of this adaptive scheme is established using Lyapunov stability tools, where we guarantee the global stability of the resulting closed-loop system, in the sense that all signals involved are uniformly bounded. The simulation results for a Duffing forced-oscillation system show better performances, i.e. tracking error and control effort can be made smaller.
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