Bipartite-Tracking Quasi-Consensus of Nonlinear Uncertain Multi-Agent Systems: Neural Network-Based Adaptive State-Constraint Impulsive Control Approach

Abstract In the engineering application of multi-agent systems (MASs), the uncertain dynamic and the actuator saturation are inevitable. Considering these factors, the bipartite-tracking quasi-consensus of nonlinear uncertain MASs over signed graph is discussed in this paper. Two kinds of neural network-based adaptive state-constraint impulsive control protocols are proposed, where the communication instant between the leader and followers only takes place at some discrete time. Considering radial basis function neural networks (RBFNNs) having superior approximation ability, we design an adaptive weight updating strategy to compensate the uncertain nonlinear dynamic of the system. By means of linear matrix inequality (LMI), convex analysis, impulsive system theory and Lyapunov stability theory, we derive some simple sufficient conditions for the bipartite-tracking quasi-consensus under the assumption that the communication topology is structurally balanced. Further, we estimate the region of attraction of the error system between the leader and followers. Two simulation examples are also provided to show the effectiveness of the proposed protocols.