Adaptive robust anti-disturbance control for pure feedback nonlinear systems with multiple constraints

Abstract

To solve the control problem for a class of uncertain pure feedback nonlinear systems subjected to external disturbances and multiple constraints, an adaptive robust control methodology is proposed based on a disturbance observer. To handle unknown nonlinearity and external unknown disturbances, a nonlinear disturbance observer is constructed based on a radial basis function neural network, which uses a Butterworth low-pass filter to remove the algebraic loop problem. Then, to guarantee that the system can stably track the desired trajectory under the state constraints, input saturation, and prescribed tracking performance constraints, we developed a novel barrier Lyapunov function and a backstepping controller that combines an auxiliary bounded function, a Nussbaum function, and a first-order sliding-mode differentiator. Subsequently, the stability of the closed-loop system is rigorously proved by Lyapunov analysis. Finally, simulations are conducted to demonstrate the effectiveness of the proposed approach.