Optimal Leader-Following Consensus Control of Multi-Agent Systems: A Neural Network Based Graphical Game Approach

In this article, the optimal leader-following consensus control problem of multi-agent systems is solved using a novel neural network-based (NN-based) integrated heuristic dynamic programming (IHDP) algorithm under a distributed learning framework. The optimal controller is designed to find a Nash equilibrium of the multi-agent differential graphical game. According to the principle of optimality, this problem can be transformed into solving a set of coupled Hamilton-Jacobi-Bellman (HJB) equations, which are difficult to solve directly because of the nonlinearity and strong coupling of the equations. The proposed algorithm combines policy iteration (PI) and value iteration (VI), and the Nash equilibrium of performance index among agents is achieved distributedly, i.e., all agents update their control inputs only use local information. The convergence of the algorithm is rigorously proved. Neural network (NN) approximation implementation is given for the unknown structures of local value functions of agents. The effectiveness of the algorithm is verified by numerical simulation.