Optimal bipartite consensus for discrete-time multi-agent systems with event-triggered mechanism based on adaptive dynamic programming

This paper proposes optimal bipartite consensus issue for discrete-time multi-agent system (DTMAS) using event-triggered control (ETC) and quantized event-triggered control (QETC). Firstly, a novel event-triggered control strategy is introduced along with specific conditions to ensure the stability for DTMAS. Due to the intractability of the Hamilton-Jacobi-Bellman (HJB) equation, through two neural networks (NNs), the value function and optimal control are approximated by the adaptive dynamic programming (ADP) method. The weight matrix of the action neural network is updated only when triggered, while also taking into account the quantization effect of the information. The stability of the weights errors and the convergence of the system dynamic are demonstrated using Lyapunov stability theory. Finally, the practicality of the improved method is confirmed a numerical example.