论文标题
带有混合确定性和随机控制的线性季度二级阶梯式差异游戏
A Linear-Quadratic Stackelberg Differential Game with Mixed Deterministic and Stochastic Controls
论文作者
论文摘要
本文涉及线性季度（LQ）Stackelberg差异游戏，并具有混合的确定性和随机控制。在游戏中，追随者是一个随机控制器，这意味着追随者可以选择适应的随机过程，而领导者是确定性控制器，这意味着领导者可以选择仅确定性时间函数。考虑了开环stackelberg平衡解决方案。首先，追随者的最佳控制过程是通过受控随机微分方程（SDE）的最大原理获得的，该方程（SDE）是通过经典的Riccati方程的最佳状态变量和控制变量的线性函数。然后，通过对平均野外前向随机微分方程（MF-FBSDES）系统的解决方案（MF-FBSDES）的解决方案，通过直接计算成本功能的导数（MF-FBSDES）来获得领导者的最佳控制函数。它被表示为最佳状态变量的期望功能，以及通过由两个耦合的riccati方程组成的系统，对普通微分方程（ODE）的两点边界值问题的解决方案。讨论了这种新的Riccati方程系统的可溶性。
This paper is concerned with a linear-quadratic (LQ) Stackelberg differential game with mixed deterministic and stochastic controls. Here in the game, the follower is a random controller which means that the follower can choose adapted random processes, while the leader is a deterministic controller which means that the leader can choose only deterministic time functions. An open-loop Stackelberg equilibrium solution is considered. First, an optimal control process of the follower is obtained by maximum principle of controlled stochastic differential equation (SDE), which is a linear functional of optimal state variable and control variable of the leader, via a classical Riccati equation. Then an optimal control function of the leader is got via a direct calculation of derivative of cost functional, by the solution to a system of mean-field forward-backward stochastic differential equations (MF-FBSDEs). And it is represented as a functional of expectation of optimal state variable, together with solutions to a two-point boundary value problem of ordinary differential equation (ODE), by a system consisting of two coupled Riccati equations. The solvability of this new system of Riccati equation is discussed.
