Stochastic linear quadratic optimal control problems with expectation-type linear equality constraints on the terminal states

• Published in: Systems & control letters Vol. 177; p. 105551
• Main Authors: Zhang, Haisen, Zhang, Xianfeng
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.07.2023
• Subjects: Expectation-type linear equality constraint; Kalman-type rank condition; Lagrangian duality; Riccati equation; Stochastic linear quadratic optimal control problem; Stochastic linear quadratic optimal control problem; Lagrangian duality; Kalman-type rank condition; Riccati equation; Expectation-type linear equality constraint
• ISSN: 0167-6911; 1872-7956
• DOI: 10.1016/j.sysconle.2023.105551

A stochastic linear quadratic (LQ) optimal control problem with an expectation-type linear equality constraint on the terminal state is considered. Under the solvability condition on a stochastic Riccati equation and a surjectivity condition on the linear constraint mapping, the constrained stochastic LQ problem is solved completely by the Lagrangian duality theory. Some equivalent characterizations of the surjectivity condition are discussed by the controllability theory of linear control systems. Especially, the equivalence between the surjectivity condition and a Kalman-type rank condition is proved under proper conditions.