Abstract:
Finite/fixed-time controls for multiagent systems (MASs) in cooperative and competitive networks have been discussed intensively, and the structural balance and gauge tra...Show MoreMetadata
Abstract:
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.
Published in: IEEE Transactions on Systems, Man, and Cybernetics: Systems ( Volume: 54, Issue: 2, February 2024)