A Kind Of Indefinite Stochastic Linear Quadratic Optimal Control Problem With Incomplete Data

The linear quadratic optimal control problems constitute an extremely important class of optimal control problems, since they can model many problems in applications, and more importantly, many nonlinear control problems can be reasonably approximated by the linear quadratic problems. On the other hand, solutions of linear quadratic problems exhibit elegant properties due to their simple and nice structures. Many classical results have been got from deterministic case to the stochastic case and written to the books about modern control theory.A stochastic linear quadratic(LQ)control problem is indefinite when the cost weighting matrices for the state and the control are allowed to be indefinite. Indefinite stochastic LQ theory has been extensively developed and has found interesting applications in finance.This paper mainly discusses a kind of indefinite stochastic linear quadratic optimal control problem with incomplete data, which can be described as:Minimize subject to Here Q(t), F are indefinite symmetric matrices,R(t) is a positive semidefinite symmetric matrix.We will use the so-called "principle of separation" (see[9])to decompose the optimal control problem with incomplete data into two problems: a filtering problem and a control problem with complete data.Then a type of Riccati equation...