A Leader-Follower Stochastic Linear Quadratic Differential Game
A Leader-Follower Stochastic Linear Quadratic Differential Game
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DOI：
10.1137/s0363012901391925
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发表时间：
2002-04
期刊：
影响因子：
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通讯作者：
J. Yong
中科院分区：
文献类型：
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作者：
J. Yong
研究了一类领导者-跟随者随机微分对策，其中状态方程为线性Ito型随机微分方程，代价泛函为二次型。我们允许系统的系数和代价泛函的系数是随机的，控制进入状态方程的扩散，并且代价泛函中的控制的权重矩阵不一定是正定的。只考虑了所谓的开环策略。因此，跟随者首先借助随机Riccati方程来求解随机线性二次型(LQ)最优控制问题。然后，领导转向求解一个正反向随机微分方程的随机LQ问题。如果这样的LQ问题是可解的，则得到了二人主从随机微分对策的开环解。此外，证明了如果一个新的随机Riccati方程是可解的，则开环解允许状态反馈表示。
A leader-follower stochastic differential game is considered with the state equation being a linear Ito-type stochastic differential equation and the cost functionals being quadratic. We allow that the coefficients of the system and those of the cost functionals are random, the controls enter the diffusion of the state equation, and the weight matrices for the controls in the cost functionals are not necessarily positive definite. The so-called open-loop strategies are considered only. Thus, the follower first solves a stochastic linear quadratic (LQ) optimal control problem with the aid of a stochastic Riccati equation. Then the leader turns to solve a stochastic LQ problem for a forward-backward stochastic differential equation. If such an LQ problem is solvable, one obtains an open-loop solution to the two-person leader-follower stochastic differential game. Moreover, it is shown that the open-loop solution admits a state feedback representation if a new stochastic Riccati equation is solvable.