Adaptive Neural Network Dynamic Surface Control for a Class of Time-Delay Nonlinear Systems With Hysteresis Inputs and Dynamic Uncertainties.

Abstract

In this paper, an adaptive neural network (NN) dynamic surface control is proposed for a class of time-delay nonlinear systems with dynamic uncertainties and unknown hysteresis. The main advantages of the developed scheme are: 1) NNs are utilized to approximately describe nonlinearities and unknown dynamics of the nonlinear time-delay systems, making it possible to deal with unknown nonlinear uncertain systems and pursue the L∞ performance of the tracking error; 2) using the finite covering lemma together with the NNs approximators, the Krasovskii function is abandoned, which paves the way for obtaining the L∞ performance of the tracking error; 3) by introducing an initializing technique, the L∞ performance of the tracking error can be achieved; 4) using a generalized Prandtl-Ishlinskii (PI) model, the limitation of the traditional PI hysteresis model is overcome; and 5) by applying the Young's inequalities to deal with the weight vector of the NNs, the updated laws are needed only at the last controller design step with only two parameters being estimated, which reduces the computational burden. It is proved that the proposed scheme can guarantee semiglobal stability of the closed-loop system and achieves the L∞ performance of the tracking error. Simulation results for general second-order time-delay nonlinear systems and the tuning metal cutting system are presented to demonstrate the efficiency of the proposed method.