Stochastic Linear-Quadratic Optimal Control Theory: Open-Loop and Closed-Loop Solutions by Jingrui Sun & Jiongmin Yong

Author:Jingrui Sun & Jiongmin Yong
Language: eng
Format: epub
ISBN: 9783030209223
Publisher: Springer International Publishing

Since the -norm of is dominated by the -norm of , it is expected that the -boundedness of will lead to the open-loop solvability of Problem (SLQ). In fact, an even stronger result holds.

Proposition 2.6.3

Let (H1)–(H2) hold and assume (2.6.3). Let be the family defined by (2.6.6). If

(2.6.19)

then the Riccati equation (2.4.1) is regularly solvable on [0, T]. Consequently, Problem (SLQ) is closed-loop solvable.

Proof

Fix an arbitrary and let be the solution to

By Itô’s formula, we have for any ,

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