Adaptive Fuzzy Containment Control for Multiagent Systems With State Constraints Using Unified Transformation Functions

In this article, the finite-time containment control problem of the nonlinear multiagent systems (MAS) is investigated, in which the follower agents are subjected to full state constraints. The fuzzy logic system is employed to approximate the uncertain dynamic of the nonlinear MAS. A new nonlinear transformation function (NTF) is proposed, which serves as a unified tool for coping with the systems subjected to state constraints and no constraint. By combing the variable transformation with the proposed NTF, the original systems with state constraints are converted into the equivalent free-constrained systems. Moreover, as long as the boundedness of the states in transformed systems is guaranteed, the states of the original MAS do not transgress the preassigned boundaries. Based on the finite-time stability theory, the adaptive fuzzy control scheme is constructed for the transformed systems. It is proved that the outputs of all the followers are driven to converge to the convex hull spanned by the leaders in a finite time, and all the signals in the closed-loop systems are bounded in sense of mean square. The full state constraints for the followers are not violated all the time. Especially, the control structure does not need to change even there is no constraint imposes on the state. Finally, simulation examples are given to verify the effectiveness of the proposed finite-time control scheme.