Robust adaptive nonlinear control for uncertain control-affine systems and its applications

Abstract

This paper addresses the robust tracking control problem for a class of uncertain nonlinear systems with time-varying parameters, perturbed by external disturbances. The unknown time-varying parameters and disturbances are neither required to be periodic nor to have known bounds. Depending on the characteristics of disturbance signals, two adaptive-based control algorithms are developed. First, an adaptive H ∞ control is designed that achieves: (i) an H ∞ tracking performance when the external disturbances are L 2 signals, and (ii) the convergence of tracking error to zero if the disturbances are bounded and L 2 signals. Then a novel adaptive control algorithm is proposed, only with the assumption of boundedness of disturbances, to drive the tracking error to zero. The designed tracking controllers are then used for controlling a cart-pendulum system, as an underactuated mechanical system, and chaos synchronization of uncertain Genesio-Tesi chaotic system. Numerical simulations are also given to demonstrate the effectiveness of the proposed control schemes. © 2008 Springer Science+Business Media B.V.