Adaptive fuzzy sliding mode control with GA-based reaching laws

Based on fuzzy approximators of nonlinear functions, a stable sigma -adapti ve fuzzy sliding mode continuous control with a fixed continuous reaching l aw is proposed in this paper for a class of nonlinear plants. In a comparis on with most existing adaptive fuzzy sliding mode control schemes where the parameter projection algorithm is often involved in the adaptive laws to p revent the estimated value of the input gain function from evolving into ze ro, the proposed control law has shown its success and simplicity in tackli ng the case when the value of the estimated input gain function becomes zer o during on-line operations. Moreover, based on the genetic algorithm (GA) approach to the optimal design of parameters of the reaching law, the reach ing dynamics can be significantly improved during the reaching phase. The b ounding parameters of the model approximation error and the external distur bance are all regarded as unknown constants in this paper, and adaptive law s for them are devised for tracking purpose. Based on Lyapunov's stability theory the proposed controller has been shown to render the tracking error to an arbitrarily small neighborhood of zero. This can be illustrated by th e simulation results for an inverted pendulum system. (C) 2001 Elsevier Sci ence B.V. All rights reserved.