Adaptive Neural Dynamic Surface Control of Pure-Feedback Nonlinear Systems With Full State Constraints and Dynamic Uncertainties

In this paper, adaptive neural dynamic surface control (DSC) is developed using radial basis function neural networks (NNs) for a class of pure-feedback nonlinear systems with full state constraints and dynamic uncertainties. Based on 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 dealt with using a dynamic signal. Using modified DSC and mean value theorem as well as Nussbaum function, two adaptive NN control schemes are proposed 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. It is shown that all the signals in the closed-loop system are semi-globally uniformly ultimately bounded, and the full state constraints are not violated. Two numerical examples are provided to illustrate the effectiveness of the proposed approach.