Distributed sliding mode consensus control for multiple discrete-Time Euler-Lagrange systems

Abstract

This paper studies the consensus problem for multiple discrete-time Euler-Lagrange (DTEL) systems via distributed sliding mode control under a directed graph. Different from the existing work, we transform the DTEL system into a discrete-time second-order nonlinear system through the famous Euler’s first-order approximation method, and a local discrete-time disturbance observer (DTDO) is introduced to estimate both model uncertainties and external disturbances. In addition, a novel integral sliding surface is proposed to guarantee that the consensus error is asymptotically stable when agents move on the sliding surface. Based on such a sliding manifold combined with the proposed DTDO, a distributed sliding mode controller is constructed. Meanwhile, a sufficient condition is derived to ensure the existence of the quasi-sliding mode motion. Finally, numerical simulations of the two-link robot arm’s system are carried out to verify the effectiveness of the proposed control algorithm.