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Finite/fixed-time controls for multiagent systems (MASs) in cooperative and competitive networks have been discussed intensively, and the structural balance and gauge transformation play a crucial role in analyzing the finite/fixed-time bipartite cooperative behavior of MASs. However, the structural balance for a large-sized network is not easy to verify, and it is uncertain whether the gauge transformation is feasible for nonlinear networks. Without adopting the gauge transformation, this article considers finite/fixed-time bipartite controls of nonlinear neural networks (NNs) with cooperative and competitive interactions. A matrix $M$ in cooperative networks is extended to a general one in cooperative and competitive networks to design quadratic Lyapunov functions. On this basis, the finite/fixed-time bipartite synchronization criteria and adjustment times are obtained, which avoids adopting the gauge transformation in a nonlinear system. The negative cycle is found to have a very important effect on the dynamic behavior of NNs. Numerical examples validate the proposed bipartite controls of NNs in a signed graph.

Interval bipartite consensus of multiagents described by signed graphs has received extensive concern recently, and the rooted cycles play a critical role in stabilization, while the structurally balanced graphs are essential to achieve bipartite consensus. However, the gauge transformation used in the linear system is no longer feasible in the nonlinear case. This article addresses interval bipartite synchronization of multiple neural networks (NNs) in a signed graph via a Lyapunov-based approach, extending the existing work to a more practical but complicated case. A general matrix M in signed graphs is introduced to construct the novel Lyapunov functions, and sufficient conditions are obtained. We find that the rooted cycles and the structurally balanced graphs are essential to stabilize and achieve bipartite synchronization. More importantly, we discover that the nonrooted cycles are crucial in reaching interval bipartite synchronization, not previously mentioned. Several examples are presented to illustrate interval bipartite synchronization of multiple NNs with signed graphs.

The time-triggered impulsive controls were widely used to study the collective behavior of homogeneous dynamical networks due to their low control cost, which was a bit conservative in the occupation of communication channels. This article addresses designing the event-triggered impulsive controls for the quasisynchronization, namely, a weak cooperative behavior with the synchronization error no more than a positive constant in the leader-following heterogeneous dynamical network, which thus can reduce the occupation of resources significantly. The centralized and distributed impulsive controls are designed to lead the followers to synchronize approximately to the leader within a nonzero bound, where the impulsive instants are triggered, respectively, by the global or local state-dependent conditions. Numerical results are put forward to verify the effectiveness of the proposed methods.

This brief is primarily devoted to the predefined-time average consensus of heterogeneous nonlinear leaderless multi-agent systems (MASs). Firstly, the predefined-time stability for a class of fixed-time stable systems is studied, which greatly improves the overestimation for the settling time of the fixed-time stability. Moreover, compared with the classical conclusions, our results are more suitable for the control of nonlinear MASs. Then, on the basis of the proposed stability analysis, a simple control algorithm is designed for ensuring the predefined-time average consensus of the system under consideration. With this predefined-time approach, any desired settling time can be achieved by adjusting the control gain. Finally, numerical simulation is shown to support the theoretical analysis.