Study on Indefinite Stochastic Linear Quadratic Optimal Control with Inequality Constraint

[摘要] This paper studies the indefinite stochastic linear quadratic (LQ) optimal control problem with an inequality constraintfor the terminal state. Firstly, we prove a generalized Karush-Kuhn-Tucker (KKT) theorem under hybrid constraints. Secondly, a new type of generalized Riccati equations is obtained, based on which a necessary condition (it is also a sufficient condition under stronger assumptions) for the existence of an optimal linear state feedback control is given by means of KKT theorem. Finally, we design a dynamic programming algorithm to solve the constrained indefinite stochastic LQ issue.

[学科分类] 应用数学