Fixed-Time Consensus for Disturbed Fractional- Order Multiagent Systems With Digraphs: An Estimator-Based Continuous Approach

The aim of this study is to examine the fixed-time consensus problem (including the leaderless consensus problem and tracking problem) of disturbed fractional-order multiagent systems (FOMASs) under general directed graphs (digraphs). In the tracking problem of a disturbed FOMAS, a dynamic leader subjected to nonzero input is considered, where the input is upper-bounded and unknown to other agents. To solve the leaderless consensus problem, a continuous control law using a disturbance estimator is first developed as the fully distributed leaderless consensus algorithm. Then, to solve the tracking problem, a fully distributed tracking algorithm using the disturbance estimator and a leader estimator is further developed, where the leader estimator is designed to estimate the dynamic leader. It should be noted that the developed fully distributed leaderless consensus and tracking algorithms possess chattering avoidance, zero-error fixed-time convergence, and complete disturbance-rejecting properties. In addition, a rigorous stability analysis based on the fixed-time Lyapunov stability theory is conducted, and the upper bounds of the convergence times are estimated explicitly, which are irrelevant to any initial conditions. Finally, numerical simulation results are provided to validate the developed algorithms.