中文摘要：

研究了一类连续时间广义随机仿射系统的线性二次（Linear Quadratic,LQ）控制问题.在定义了广义随机系统稳定性的相关概念后,通过一个线性矩阵不等式（Linear Matrix Inequality,LMI）给出了系统稳定性的条件.然后,利用Riccati方程法分别研究了有限时间广义随机仿射系统的LQ问题和无限时间广义随机系统的LQ问题,得到了有限时间最优反馈控制的存在条件等价于一个推广的微分Riccati方程和一个推广的倒向微分方程存在解,而对应的无限时间最优反馈控制的存在条件等价于一个推广的代数Riccati方程存在解,同时给出了最优反馈控制的显式表达及最优性能指标值.

英文摘要：

Linear quadratic control of a class of continuous-time singular stochastic affine systems is investigated. After establishing some concepts of the stability for stochastic singular systems,the condition of the stability is presented by means of a linear matrix inequality. Then,by utilizing Riccati equation approach,the existent conditions of optimal feedback control in finite horizon and infinite horizon are respectively obtained by means of a generalized differential Riccati equation or a generalized algebraic Riccati equation. And explicit expressions of the optimal feedback controls and optimal cost function are given.