Adaptive Neural Network Control of Uncertain Systems with Full State Constraints and Unknown Gain Sign

Abstract

In this paper, adaptive neural network control is proposed based on improved dynamic surface control (DSC) method and the approximation capability of radial basis function (RBF) neural networks (NNs) for a class of uncertain constrained pure-feedback nonlinear systems with unmodeled dynamics and unknown gain sign. By constructing a one to one nonlinear mapping, the pure-feedback system with full state constraints is transformed into a novel pure-feedback system without state constraints. The dynamic uncertainties are handled using an auxiliary dynamic signal. Using mean value theorem and Nussbaum function, an adaptive NN control scheme is developed based on the transformed system. The designed control strategy removes the conditions that the upper bound of the control gain is known, and the lower bounds and upper bounds of the virtual control coefficients are known. By theoretical analysis, all the signals in the closed-loop system are shown to be semi-globally uniformly ultimately bounded (SGUUB), and the full state constraints are not violated. A numerical example is provided to demonstrate the effectiveness of the proposed method.