Volume 26, 2020
|Number of page(s)||23|
|Published online||10 December 2020|
Optimal control for controllable stochastic linear systems
Department of Statistics and Finance, University of Science and Technology of China,
230026, PR China.
2 Department of Mathematics, Southern University of Science and Technology, Shenzhen, Guangdong 518055, PR China.
3 Department of Mathematics and SUSTech International center for Mathematics, Southern University of Science and Technology, Shenzhen, Guangdong 518055, PR China.
* Corresponding author: email@example.com
Accepted: 11 May 2020
This paper is concerned with a constrained stochastic linear-quadratic optimal control problem, in which the terminal state is fixed and the initial state is constrained to lie in a stochastic linear manifold. The controllability of stochastic linear systems is studied. Then the optimal control is explicitly obtained by considering a parameterized unconstrained backward LQ problem and an optimal parameter selection problem. A notable feature of our results is that, instead of solving an equation involving derivatives with respect to the parameter, the optimal parameter is characterized by a matrix equation.
Mathematics Subject Classification: 49N10 / 93E20 / 93E24 / 93B05
Key words: Linear-quadratic / optimal control / controllability / controllability Gramian / Lagrange multiplier / optimal parameter / Riccati equation
© EDP Sciences, SMAI 2020
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