Mixed H2/H∞ Control With Event-Triggered Mechanism for Nonlinear Stochastic Systems With Closed-Loop Stackelberg Games
Zhongyang Ming, Huaguang Zhang, Juan Zhang, Yanhong Luo · IEEE Transactions on Systems Man and Cybernetics Systems · 2023
In this article, the mixed$H_{2}/H_{\infty }$control problem with closed-loop Stackelberg games for nonlinear stochastic systems is studied. With the help of the value functions of leader and follower, the Stackelberg game problem is transformed into the numerical solution of Hamilton–Jacobi (HJ) equations with generalized Hamiltonian functions. On the premise of ensuring that the system state is uniformly ultimate bounded (UUB), an adaptive neural networks (NNs) algorithm is proposed to approach the closed-loop Stackelberg equilibrium. This is the first time that adaptive dynamic programming (ADP) is used to solve the closed-loop Stackelberg games control problem of nonlinear stochastic systems. Further, in order to reduce computational load and save communication resources, the event-triggering control strategy is obtained. Moreover, a novel stochastic comparison lemma is given, which is used to exclude Zeno behavior during the learning process. Finally, a simulation example is used to demonstrate the usefulness of the suggested near-optimal control scheme.