Fuzzy Distributed Containment Tracking of Multi-Agent Systems with Uncertain Granular Fuzzy Linear Dynamics

This paper investigates the distributed containment tracking problem in linear multi-agent systems with fuzzy uncertainty in agents’ dynamics. The fuzzy granular uncertainty is in the form of a fuzzy number with a known membership degree for any value in the range of uncertainty. Hence, the errors of containment tracking are also fuzzy numbers. In this paper, the new concepts of fuzzy convex hull and fuzzy containment tracking are introduced. We present a crisp containment control protocol to achieve the fuzzy containment tracking. Sufficient conditions in the form of linear matrix inequalities are proposed to guarantee that fuzzy containment problem is solved with the suggested containment protocol. This means that the fuzzy state trajectories of the followers converge to the fuzzy convex hull constructed by the leaders’ states via employing the suggested method. The major merit of the suggested protocol is that the crisp gain matrix which is introduced can be practically implemented on any microprocessors. Simulation examples confirm the performance of the offered method.