Linear-Quadratic Optimal Controls in Finite Horizons

  • Jingrui SunEmail author
  • Jiongmin Yong
Part of the SpringerBriefs in Mathematics book series (BRIEFSMATH)


This chapter is devoted to a study of stochastic linear-quadratic optimal control problems in a finite horizon from two points of view: open-loop and closed-loop solvabilities. A simple example shows that these two solvabilities are essentially different. Open-loop solvability is established by studying the solvability of a constrained linear forward-backward stochastic differential equation. Closed-loop solvability is reduced to the existence of a regular solution to the associated differential Riccati equation, which is implied by the uniform convexity of the quadratic cost functional. The relation between open-loop and closed-loop solvabilities, as well as some other aspects, such as conditions ensuring the convexity of the cost functional, finiteness of the problem and construction of minimizing sequences, are also discussed.


Linear-quadratic optimal control Finite horizon Open-loop solvability Closed-loop solvability Differential Riccati equation Uniform convexity Finiteness 

Copyright information

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of MathematicsSouthern University of Science and TechnologyShenzhenChina
  2. 2.Department of MathematicsUniversity of Central FloridaOrlandoUSA

Personalised recommendations