Feedback Stackelberg strategies for the discrete-time mean-field stochastic systems in infinite horizon
Feedback Stackelberg strategies for the discrete-time mean-field stochastic systems in infinite horizon
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DOI：
10.1016/j.jfranklin.2019.05.012
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发表时间：
2019-07
期刊：
影响因子：
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通讯作者：
Yaning Lin
中科院分区：
文献类型：
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作者：
Yaning Lin
本文研究了无穷时域离散平均场随机系统的反馈Stackelberg策略。首先研究了从动件的最优控制问题。利用离散时间线性二次型（LQ）平均场随机最优控制理论，基于两个耦合的广义代数Riccati方程（GARES）的稳定解，给出了跟随器最优解可解的充分条件，并得到了最优控制.然后，领导者的优化转化为一个有约束的最优控制问题。应用Karush-Kuhn-Tucker（KKT）条件，导出了Stackelberg策略存在唯一的必要条件，并基于交叉耦合随机代数方程组（CSAE）的解（Ki，K^ i），i= 1，2，将Stackelberg策略表示为包含状态及其均值的线性反馈形式.提出了一种迭代算法来有效地计算CSAE的解。最后，通过算例验证了该算法的有效性.
This paper deals with the feedback Stackelberg strategies for the discrete-time mean-field stochastic systems in infinite horizon. The optimal control problem of the follower is first studied. Employing the discrete-time linear quadratic (LQ) mean-field stochastic optimal control theory, the sufficient conditions for the solvability of the optimization of the follower are presented and the optimal control is obtained based on the stabilizing solutions of two coupled generalized algebraic Riccati equations (GAREs). Then, the optimization of the leader is transformed into a constrained optimal control problem. Applying the Karush-Kuhn-Tucker (KKT) conditions, the necessary conditions for the existence and uniqueness of the Stackelberg strategies are derived and the Stackelberg strategies are expressed as linear feedback forms involving the state and its mean based on the solutions (K i, K^ i), i= 1, 2 of a set of cross-coupled stochastic algebraic equations (CSAEs). An iterative algorithm is put forward to calculate efficiently the solutions of the CSAEs. Finally, an example is solved to show the effectiveness of the proposed algorithm.