Model Reference Adaptive Control for Nonlinear Systems in the Presence of Unknown External Disturbances

The present study aims to investigate the model reference adaptive control for the continuous-time nonlinear systems in the presence of external disturbances. The reference model is regarded as a linear system. In addition, the external disturbances are assumed to be unknown and bounded. To design the controller, the nonlinear system is considered to be a linear system with uncertainties, which are approximated by using radial basis function neural networks. These uncertainties involve unknown external disturbances and system linearization error. As a result, the adaptive controller can compensate system linearization error as well as unknown external disturbances. Lyapunov theory is used for the stability analysis of the proposed controller. Consequently, the proposed controller guarantees that the nonlinear system tracks the reference model in the presence of unknown external disturbances. Finally, the simulation results of a numerical example and a practical example, which is the simulation of Chua's chaotic system, are given to evaluate the performance of the proposed controller.