Journal
SYSTEMS & CONTROL LETTERS
Volume 161, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.sysconle.2022.105149
Keywords
Forward-backward stochastic differential equation; Stochastic linear-quadratic problem; Stochastic optimal control; Infinite horizon; Stochastic differential delay equation
Funding
- National Key R&D Program of China [2018YFA0703900]
- National Natural Science Foundation of China [11871310]
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This paper investigates a class of coupled forward-backward stochastic differential equations (FBSDEs) on infinite horizon involving time delays and time advancements, and achieves the unique solvability by introducing a randomized Lipschitz condition and a randomized monotonicity condition. The theoretical result is then applied to a linear-quadratic problem of a time-delayed system with random coefficients, leading to an explicit expression of the unique optimal control.
This paper is concerned with a class of coupled forward-backward stochastic differential equations (FBSDEs, for short) involving time delays and time advancements on infinite horizon. By introducing a randomized Lipschitz condition and a randomized monotonicity condition, the unique solvability of FBSDEs is obtained. Then the theoretical result is applied to a linear-quadratic (LQ, for short) problem of a time-delayed system with random coefficients. An explicit expression of the unique optimal control is obtained. (C) 2022 Elsevier B.V. All rights reserved.
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