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In this paper, a bipartite consensus problem is considered for a high-order multiagent system with cooperative-competitive interactions and unknown time-varying disturbances. A signed graph is used to describe the interaction network associated with the multiagent system. The unknown disturbances are expressed by linearly parameterized models, and distributed adaptive laws are designed to estimate the unknown parameters in the models. For the case that there is no exogenous reference system, a fully distributed adaptive control law is proposed to ensure that all the agents reach a bipartite consensus. For the other case that there exists an exogenous reference system, another fully distributed adaptive control law is also developed to ensure that all the agents achieve bipartite consensus on the state of the exogenous system. The stability of the closed-loop multiagent systems with the 2 proposed adaptive control laws are analyzed under an assumption that the interaction network is structurally balanced. Moreover, the convergence of the parameter estimation errors is guaranteed with a persistent excitation condition. Finally, simulation examples are provided to demonstrate the effectiveness of the proposed adaptive bipartite consensus control laws for the concerned multiagent system. KEYWORDSbipartite consensus, coopetition networks, distributed adaptive control, high-order multiagent systems 2868

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In this paper, an antisynchronization problem is considered for an array of linearly coupled reaction-diffusion neural networks with cooperative-competitive interactions and time-varying coupling delays. The interaction topology among the neural nodes is modeled by a multilayer signed graph. The state evolution of a neuron in each layer of the coupled neural network is described by a reaction-diffusion equation (RDE) with Dirichlet boundary conditions. Then, the collective dynamics of the multilayer neural network are modeled by coupled RDEs with both spatial diffusion coupling and state coupling. An edge-based adaptive antisynchronization strategy is proposed for each neural node to achieve antisynchronization by using only local information of neighboring nodes. Furthermore, when the activation functions of the neural nodes are unknown, a linearly parameterized adaptive antisynchronization strategy is also proposed. The convergence of the antisynchronization errors of the nodes is analyzed by using a Lyapunov-Krasovskii functional method and a structural balance condition. Finally, some numerical simulations are presented to demonstrate the effectiveness of the proposed antisynchronization strategies.

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