Fixed-time adaptive tracking control of two moving targets for a class of non-linear multi-agent systems

Abstract

In this research paper, the fixed-time adaptive tracking of two moving targets for a class of unknown non-linear multi-agent systems based on a distributed competition approach is studied. Each agent simultaneously participates in two competitions based on the k-Winner Take All (k-WTA) approach to obtain its allocation status. Using a mean value estimator, the agent can calculate its allocation status only by its neighbor's information. Since an agent can only track one target, an extended tracking error is introduced, where if the agent wins one of the competitions, it will track the assigned target, and if the agent wins both competitions, by selecting one of the targets, track the selected target. Also, the agent which is not win any competitions, return to a specified point. Then, using neural networks and adaptive techniques, an adaptive fixed-time controller is introduced for the agents to track the target based on the allocation status or to return to the specified point. Analysis of the stability of the closed-loop system through the Lyapunov theorem is investigated. Finally, a simulation study to show the efficiency of the theoretical results is presented.