Discrete-Time Sliding Mode-Based Finite-Time Trajectory Tracking Control of Underactuated Surface Vessels With Large Sampling Periods

Abstract

This paper investigates finite-time trajectory tracking control based on discrete-time sliding mode of underactuated surface vessels with compound disturbances comprising model parameter uncertainties and environmental disturbances under large sampling periods. By introducing the second-order Runge-Kutta method without complex operation to discretize the continuous-time vessel model, a high-precision discrete-time model is first obtained to ensure the controller design accuracy in discrete-time systems. Then, a novel finite-time discrete position tracking controller is developed by constructing a coordinate transformation to address the underactuating problem of surface vessels and convert position tracking error into expected velocity command. The compound disturbance is estimated and compensated by a high-order finite-time discrete disturbance observer. The current research on large sampling period control faces the shortcoming of adjusting parameters repeatedly to accommodate varying sampling periods while balancing convergence speed. To address it and enhance control system adaptability to large sampling periods while reducing operating losses and communication burdens on the sensing system, a novel adaptive reaching law is proposed based on existence conditions of the discrete-time sliding mode control system. Given this, a discrete-time sliding mode based finite-time velocity tracking controller is proposed to achieve stable velocity tracking over a large sampling period range. Finally, all tracking errors are demonstrated to converge within a finite time to a small region near zero. Two examples of comparative simulations validate the efficacy of the developed control strategy.