论文标题
一般不确定的后退随机线性季度最佳控制问题
General Indefinite Backward Stochastic Linear-Quadratic Optimal Control Problems
论文作者
论文摘要
研究了一般的向后随机线性最佳控制问题，其中状态方程和成本功能都包含非均匀项。问题的主要特征是，成本函数中的加权矩阵被允许在控制中不确定，并且存在状态过程。获得了问题的必要条件，可以获得问题的可溶性，并得出了前向后随机微分方程的最佳控制表征。通过RICCATI方程方法，开发了用于构建最佳控制的一般过程，并明确获得值。
A general backward stochastic linear-quadratic optimal control problem is studied, in which both the state equation and the cost functional contain the nonhomogeneous terms. The main feature of the problem is that the weighting matrices in the cost functional are allowed to be indefinite and cross-product terms in the control and the state processes are present. Necessary and sufficient conditions for the solvability of the problem are obtained, and a characterization of the optimal control in terms of forward-backward stochastic differential equations is derived. By a Riccati equation approach, a general procedure for constructing optimal controls is developed and the value function is obtained explicitly.
