Robust Adaptive Fixed-Time Consensus for Nonlinear High-Order Multi-Agent Systems

This paper investigates the consensus problem of leader-follower nonlinear high-order multi-agent systems through a fully distributed approach. A distributed consensus tracking control scheme is proposed, embedding a fixed-time convergent command filter with adaptive gain to ensure that the filter error ultimately reaches the origin. To tackle the challenges posed by unknown bounds of system nonlinearities and external disturbances, a robust control protocol is developed, incorporating an adaptive mechanism to implement compensatory action instead of directly estimating the lumped uncertainty. A notable feature of the proposed approach lies in its capability to determine the settling time bound without any global information, including the number of nodes, the eigenvalue of the Laplacian matrix, and other unknown parameters. The efficacy of the developed methodology is validated through numerical simulations and physical experiment conducted on a multi-motor system. Note to Practitioners—In contemporary engineering systems, the consensus tracking control of high-order multi-agent systems has emerged as a significant research topic. This paper proposes a fully distributed control scheme to achieve fixed-time consensus tracking. Unlike conventional finite-time and fixed-time approaches, the upper bound of the convergence time in this paper is independent of any global information and system’s initial states. Practical operational environments frequently introduce complex nonlinearities and disturbances into physical systems. To address this challenge, an adaptive mechanism is integrated into the robust control protocol. Importantly, the number of adaptive parameters remains fewer, irrespective of the number of uncertain parameters or the dimension of disturbances and nonlinearities. The feasibility of the proposed scheme is demonstrated via a physical experiment executed on a multi-motor system. In future research, we will simultaneously consider input saturation constraints.