Infinite time linear quadratic stackelberg game problem for unknown stochastic discrete‐time systems via adaptive dynamic programming approach

Abstract

AbstractIn this paper, we propose an adaptive dynamic programming (ADP) approach to solve the infinite horizon linear quadratic (LQ) Stackelberg game problem for unknown stochastic discrete‐time systems with multiple decision makers. Firstly, the stochastic LQ Stackelberg game problem is converted into the deterministic problem by system transformation. Next, a value iteration ADP approach is put forword and the convergence is given. Thirdly, in order to implement the iterative method, back propagation neural network (BPNN) is chosen to design model network, critic network and action network to approximate the unknown systems, objective functions and Stackelberg strategies. Finally, simulation results show that the algorithm is effective.