  In this paper, a new on-line scheme is presented to design the optimal
coordination control for the consensus problem of multi-agent differential
games by fuzzy adaptive dynamic programming (FADP), which brings together game
theory, generalized fuzzy hyperbolic model (GFHM) and adaptive dynamic
programming. In general, the optimal coordination control for multi-agent
differential games is the solution of the coupled Hamilton-Jacobi (HJ)
equations. Here, for the first time, GFHMs are used to approximate the solution
(value functions) of the coupled HJ equations, based on policy iteration (PI)
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 rchitecture for each agent (which eliminates the action network
model compared with dual-network architecture), it is a more reasonable
architecture for multi-agent systems. Furthermore, the approximation solution
is utilized to obtain the optimal coordination controls. 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.
