Hierarchical Decision Problems for Non-Affine Multi-Player Systems

Adaptive dynamic programming is used in this paper to solve the hierarchical decision problem for non-affine multi-player systems. A new affine system is formed by adding control dynamics to the original system. To solve the hierarchical decision problem of the original system, we modeled it as a Stackelberg game in the new system. Adaptive dynamic programming is used to approximate the value functions. The stability of the system is analyzed according to Lyapunov theory, which leads to the conclusion that both the system states and the weight errors are uniformly ultimately bounded. Finally, matlab simulation is used to verify the conclusion.