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In this paper, an enhanced adaptive fuzzy control (AFC) strategy with guaranteed convergence of an optimal fuzzy approximation error (FAE) is presented for a class of uncertain nonlinear systems in the general Brunovsky form. Based on the fuzzy logic system (FLS) with variable universes of discourse, relaxed sufficient conditions that guarantee the optimal FAE being convergent are given, and the upper bound of the optimal FAE is obtained. The control singularity problem resulting from the unknown affine term is resolved by a novel fuzzy approximation equation, and the parameter adaptive law of the FLS is derived by the Lyapunov synthesis. By means of the optimal FAE bound result, it is proved that the closed-loop system achieves partially asymptotic stability under a certain selection of control parameters. The proposed approach retains all advantages of a previous similar approach under relaxed constraint conditions. Thus, it provides a more flexible solution to the AFC with optimal FAE convergence. Simulation studies have demonstrated high-precision tracking performance with smooth control input of the proposed approach.
Pan et al. (2013) studied this question.