Adaptive Predefined-Time Bipartite Consensus Tracking Control of Constrained Nonlinear MASs: An Improved Nonlinear Mapping Function Method

This work focuses on the problem of predefined-time bipartite consensus tracking control for a class of nonlinear MASs with asymmetric full-state constraints. A predefined-time bipartite consensus tracking framework is developed, where both cooperative communication and adversarial communication among neighbor agents are implemented. Different from the finite-time and the fixed-time controller design methods for MASs, the prominent advantage of the controller design algorithm presented in this work is that our algorithm can make the followers track either the output or the opposite output of the leader within the predefined time in accordance to the user requirements. In order to obtain the desired control performance, an improved time-varying nonlinear transformed function is skillfully introduced for the first time to handle the asymmetric full-state constraints and radial basis function neural networks (RBF NNs) are employed to deal with the unknown nonlinear functions. Then, the predefined-time adaptive neural virtual control laws are constructed by using the backstepping technique, while their derivatives are estimated by the first-order sliding-mode differentiators. It is theoretically testified that the proposed control algorithm not only guarantees the bipartite consensus tracking performance of the constrained nonlinear MASs in the predefined time but also remains the boundedness of all the resulting closed-loop signals. Finally, the simulation research on a practical example shows the validity of the presented control algorithm.