Prescribed-time nonsingular sliding mode control based on neural network for trajectory tracking of nonlinear systems

Abstract

Considering the influence of external time-varying disturbances on trajectory tracking control of nonlinear systems, a novel prescribed-time nonsingular sliding mode control (SMC) is proposed. Firstly, based on the definition of prescribed time stability, a lemma of practical prescribed time stability is proposed, which guarantees the system states converge to a region within the prescribed time. Secondly, a prescribed time SMC method is designed, which does not contain negative power terms in the controller and solves the singular problem. In addition, a continuous function is adopted instead of the sign function to reduce chattering, and it is also considered in the stability proof. The stability analysis shows that whatever it is in the sliding stage or the reaching stage, the tracking error is prescribed time stable. On the basis of prescribed time SMC method, the neural network (NN) is introduced to approximate the unknown model information. Finally, compared with other existing control methods, the results of simulation demonstrate that the proposed method exhibits superior performance, encompassing the achievement of prescribed time stability, the elimination of chattering, and the capability to analyze unknown model information via neural networks.