New Fixed Time Convergent Disturbance Rejection Control for Higher-order Nonlinear Systems

A new type of fixed-time disturbance rejection control is proposed to address the problems of the traditional backstepping control of higher-order nonlinear system, such as the infinite convergence time of control error, the sharp convergence slowdown near the origin, and the weak robustness in the case of unknown disturbance and system modeling error. First, a new Lyapunov theorem is presented and proved. The convergence time has a fixed upper bound, which is not dependent on initial state values. Furthermore, it has a faster convergence rate than the existing Lyapunov theorem. Then, it is combined with the traditional backstepping control, and the nonlinear disturbance observer is used to estimate the compound term of unknown external disturbance and modeling error with high precision to enhance the controller's robustness and rapidity and to reduce the steady-state error. Finally, the scheme is used for an inverted pendulum. Results indicate the superiority of the proposed scheme.