Integral Barrier Lyapunov Functions-Based Adaptive Control of Uncertain Nonlinear Systems with Unknown Control Directions and State Constraints

Abstract

This paper addresses the control problem of uncertain nonlinear systems with full state constraints and unknown control direction. In the system, different orders of system states are required to remain in their predefined set. Conventional Barrier Lypunov Functions are designed based on error dynamics and have certain limitations, whereas the introduced Integral Barrier Lyapunov Function is designed directly on the state constraint. In order to deal with the unknown control direction problem, the Nussbaum function based technique is adopted and an adaptive controller is proposed. Moreover, a neural network is constructed to estimate the uncertainties in the system. Integrating the integral barrier Lypunov function, the Nussbaum technique, and the neural network, the proposed method is able to stabilize the system without violating the state constraints. Rigorous mathematical analysis is presented to verify the controller. Finally, a simulation example illustrates the effectiveness of the proposed control method.