  In this paper, a hierarchical one-leader-multi-followers game for a class of
continuous-time nonlinear systems with disturbance is investigated by a novel
policy iteration reinforcement learning technique in which, the game model
consists both of the zero-sum and nonzero-sum games, simultaneously. An
adaptive dynamic programming (ADP), method is developed to achieve optimal
control strategy under the worst case of disturbance. This algorithm reduces
the number of neural networks which are used for estimation for about thirty
percent. The proposed algorithm uses neural networks to estimate value
functions, control policies and disturbances. Convergence analysis of the
estimations is investigated using Lyapunov theory and exploiting properties of
the Nemytskii operator. Finally, the simulation results will show effectiveness
of the developed ADP method.
