Adaptive dynamic programming-based hierarchical decision-making of non-affine systems

Abstract

In this paper, the problem of multiplayer hierarchical decision-making problem for non-affine systems is solved by adaptive dynamic programming. Firstly, the control dynamics are obtained according to the theory of dynamic feedback and combined with the original system dynamics to construct the affine augmented system. Thus, the non-affine multiplayer system is transformed into a general affine form. Then, the hierarchical decision problem is modeled as a Stackelberg game. In the Stackelberg game, the leader makes a decision based on the information of all followers, whereas the followers do not know each other's information and only obtain their optimal control strategy based on the leader's decision. Then, the augmented system is reconstructed by a neural network (NN) using input-output data. Moreover, a single critic NN is used to approximate the value function to obtain the optimal control strategy for each player. An extra term added to the weight update law makes the initial admissible control law no longer needed. According to the Lyapunov theory, the state of the system and the error of the weights of the NN are both uniformly ultimately bounded. Finally, the feasibility and validity of the algorithm are confirmed by simulation.

Keywords: Adaptive dynamic programming; Multiplayer Stackelberg game; Neural networks; Non-affine systems.