Stable adaptive output feedback controller for a class of uncertain non‐linear systems

Abstract

This study deals with design of an adaptive output feedback tracking controller for a class of non-linear systems with unknown fixed control direction. By using neural networks and deriving adaptive rules based on the steepest descent algorithm, the authors present a stable output feedback control scheme, which is applicable to a wide class of unknown complicated non-linear systems. Therefore an approach based on the dynamic back propagation algorithm is proposed to develop the adaption laws for systems with more general model structure. Using Lyapunov's direct method, uniformly ultimately boundedness of all signals of the closed-loop system is also ensured. Moreover, it is shown that the bounds on the tracking errors depend on the designing parameters. Hence, an arbitrarily small tracking error can be achieved by adjusting the parameters properly. Finally, simulation results performed on a non-affine uncertain non-linear system having internal dynamics are given to demonstrate the effectiveness of the proposed scheme and the theoretical discussions.