Control of double integrators under input saturation and disturbances

Abstract

In this paper, we study the tracking control problem for double integrators under input saturation and constant disturbances. We assume that the desired states are given by the double integrator with constant speed. To solve this problem, we propose the saturated Proportional-Integral(PI) control law. Then, by applying the Lasalle's invariance principle, we derive the sufficient conditions for the asymptotic stability of tracking error dynamics. We next extend the tracking control problem to the consensus problem for multi-agent systems. By extending the saturated PI control law, we construct the PI-based consensus control law and analyze the sufficient conditions to solve the consensus problem. Finally, the numerical example is provided to demonstrate the validity of the proposed results. © 2023 IEEE.