This article investigates admissible formation tracking for singular swarm systems under conditions of switching transmission topologies as well as the limited energy supply, where both switching transmission topologies containing a spanning tree and switching transmission topologies containing a joint spanning tree are addressed. First, a new formation control tracking protocol with switching transmission topologies is proposed to realize admissible formation tracking, where the total energy supply is predetermined. Afterwards, by a dual nonsingular transformation, the disagreement dynamics between followers and the leader is determined and the impacts of asymmetric structures of switching transmission topologies are eliminated. Sufficient conditions for admissible formation tracking design and analysis for singular swarm systems with switching transmission topologies containing a spanning tree and with switching transmission topologies containing a joint spanning tree are proposed, respectively, where the coupling relationship matrix between the total energy supply and the matrix variable is determined. Finally, two numerical simulations are presented to demonstrate the effectiveness of theoretical results.
This paper studies the problem of adaptive fuzzy proportional-integral (PI) tracking control for a class of switched nonlinear systems with dead-zone input, unknown nonlinear functions and external disturbances. By using backstepping method with fuzzy logic systems, a set of adaptive fuzzy PI tracking controllers are proposed, which have a simple structure and a clear physical meaning. The designed controllers don't need priori information of dead-zone input via introducing Nussbaum function scheme. To enhance the tracking performance, the prescribed performance technique is utilized to constrain the tracking error. The stability analysis of the closed-loop switched systems is established via common Lyapunov function, and the tracking error remains within a prescribed bound and all signals of the closed-loop system are bounded. Finally, the effectiveness of the scheme is verified by two examples.
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