Continuous Higher-Order Sliding Mode Control for a Class of n-th Order Perturbed Systems

In this brief, a general continuous higher-order sliding mode (HOSM) control algorithm is proposed for a class of n-order systems with Lipschitz disturbance, which can be regarded as a generalization of the continuous super-twisting algorithm for arbitrary relative degree with respect to the output. The proposed control algorithm only requires the information of the output and its derivatives up to the order n - 1, and can compensate the Lipschitz disturbance exactly by using a discontinuous integral term, generating a continuous homogeneous control signal and achieving finite-time convergence to a sliding mode of order n + 1. The convergence of the closed-loop system is proved rigorously by employing an explicit and directly constructed homogeneous Lyapunov function. The simulation results validate the effectiveness of the proposed method by comparing with the existing results.

Automated summary

In this paper, a general continuous higher-order sliding mode control algorithm is proposed for a class of n-order systems with Lipschitz disturbance. The algorithm only requires limited information of the output and its derivatives and can compensate the disturbance exactly, achieving finite-time convergence. Simulation results validate the effectiveness of the proposed method.