Study on Stochastic Linear Quadratic Optimal Control with Quadratic and Mixed Terminal State Constraints

[摘要] This paper studies the indefinite stochastic LQ control problemwith quadratic and mixed terminal state equality constraints, which canbe transformed into a mathematical programming problem. By meansof the Lagrangian multiplier theorem and Riesz representation theorem, themain result given in this paper is the necessary condition for indefinitestochastic LQ control with quadratic and mixed terminal equalityconstraints. The result shows that the different terminal state constraintswill cause the endpoint condition of the differential Riccati equationto be changed. It coincides with the indefinite stochastic LQ problemwith linear terminal state constraint, so the result given in this paper canbe viewed as the extension of the indefinite stochastic LQ problemwith the linear terminal state equality constraint. In order to guaranteethe existence and the uniqueness of the linear feedback control, asufficient condition is also presented in the paper. A numerical exampleis presented at the end of the paper.

[学科分类] 应用数学