Adaptive backstepping control for uncertain nonlinear systems in the presence of variable input saturation: Ensuring stability by normalization and improving the performance of parameter identification

Abstract

SUMMARYAdaptive control design schemes in the presence of input saturation have received much attention over the last two decades. However, few researchers have addressed the issue of designing the adaptive control system in the presence of unknown or variable input saturation. We propose an adaptive backstepping control method for single input uncertain nonlinear system with unknown or variable input saturation. This method uses the saturation error at previous time to estimate the saturation error at current time easily and rapidly, and the normalization based on the estimation error is introduced to ensure the stability of the whole adaptive system. We also suggest a new adaptive law to improve the performance of parameter identification in case that the uncertainty of saturation error estimation can be approximately decided. It is valid when parameters identified in the adaptive control system are taken as main design parameters of the other controllers, and especially when their accuracy has a significant influence on control performance of the whole system. Finally, simulation examples are presented to validate the effectiveness of the proposed approach.