Leader-Based Optimal Coordination Control for the Consensus Problem of Multiagent Differential Games via Fuzzy Adaptive Dynamic Programming

TLDR: For the first time, GFHMs are used to approximate the solutions (value functions) of the coupled HJ equations, based on policy iteration algorithm, and the approximation solution is utilized to obtain the optimal coordination control.

Abstract: In this paper, a new online scheme is presented to design the optimal coordination control for the consensus problem of multiagent differential games by fuzzy adaptive dynamic programming, which brings together game theory, generalized fuzzy hyperbolic model (GFHM), and adaptive dynamic programming. In general, the optimal coordination control for multiagent differential games is the solution of the coupled Hamilton-Jacobi (HJ) equations. Here, for the first time, GFHMs are used to approximate the solutions (value functions) of the coupled HJ equations, based on policy iteration algorithm. Namely, for each agent, GFHM is used to capture the mapping between the local consensus error and local value function. Since our scheme uses the single-network architecture for each agent (which eliminates the action network model compared with dual-network architecture), it is a more reasonable architecture for multiagent systems. Furthermore, the approximation solution is utilized to obtain the optimal coordination control. Finally, we give the stability analysis for our scheme, and prove the weight estimation error and the local consensus error are uniformly ultimately bounded. Further, the control node trajectory is proven to be cooperative uniformly ultimately bounded.