Discrete-time quasi-sliding mode feedback-error-learning neurocontrol of a class of uncertain systems

Abstract

The features of a novel dynamical discrete-time algorithm for robust adaptive learning in feed-forward neural networks and its application to the neuro-adaptive nonlinear feedback control of systems with uncertain dynamics are presented. The proposed approach makes a direct use of variable structure systems theory. It establishes an inner sliding motion in terms of the neurocontroller parameters, leading the learning error toward zero. The outer sliding motion concerns the controlled nonlinear system, the state tracking error vector of which is simultaneously forced towards the origin of the phase space. It is shown that there exists equivalence between the two sliding motions. The convergence of the proposed algorithm is established and the conditions are given. Results from a simulated neuro-adaptive control of Duffing oscillator are presented. They show that the implemented neurocontroller inherits some of the advantages of the variable structure systems: high speed of learning and robustness. © Springer-Verlag Berlin Heidelberg 2005.