Fixed‐time rotating consensus control of second‐order multi‐agent systems

Abstract This article investigates the fixed‐time rotating consensus problem of second‐order multi‐agent systems in both the leaderless and leader‐following cases. Specifically, in the leaderless case, a distributed controller is developed to drive all agents to reach rotating consensus in fixed‐time. In the leader‐following case, a distributed fixed‐time observer is first proposed to estimate the position of a rotating leader. Then, a local fixed‐time output feedback controller without any velocity measurements is proposed to achieve the leader‐following motion. Furthermore, an integral sliding mode control technique is applied to handle the case where the multi‐agent system is subject to time varying external disturbances. Based on the bi‐limit homogeneity method and Lyapunov theory, we prove that all the agents reach the rotating consensus within a fixed time independent of initial conditions. Finally, simulations illustrate the effectiveness of the proposed controllers.