The Optimal Feedback Control Of Linear Stochastic System And The Solution Of Quasi-Riccati Equation

It's well known that optimal control problem is one of the central themes of control science and has been widely applied in the real world such as the problem of optimal decision and production and the problem of optimal investment strategy. Therefore, the research of the existence of optimal control and the formulation of optimal feedback control is very meaningful. In this paper we study the optimal control of a multidimensional linear stochastic system with a convex and possibly non-quadratic cost function. We give out the formulation of the related Quasi-Riccati equation, get the fomulation of optimal feed-back control and discuss when the Quasi-Riccati equation has a classical solution.In Chapter 2, we introduce the linear stochastic system in detail. In Chapter 3, we give out the proof of the existence of optimal control. We get the formulation of optimal open-loop control and the first and second adjoint equations corresponding to the optimal pair. In Chapter 4, we give out the formulation of the Quasi-Riccati equation and study the solution of this equation with the help of forward-backward stochastic differential equation.