A Jump Ornstein-Uhlenbeck Bridge Based on Energy-Optimal Control and Its Self-Exciting Extension

被引：0

作者：

Yoshioka, Hidekazu ^{[1
,2
]}

Yamazaki, Kazutoshi ^{[3
]}

机构：

[1] Shimane Univ, Matsue 6900823, Japan

[2] Japan Adv Inst Sci & Technol, Grad Sch Adv Sci & Technol, Nomi, Ishikawa 9231292, Japan

[3] Univ Queensland St Lucia, Sch Math & Phys, Brisbane, Qld 4072, Australia

来源：

IEEE CONTROL SYSTEMS LETTERS | 2023年 / 7卷

关键词：

Bridges; Process control; Stochastic processes; Convergence; Mathematical models; Discharges (electric); Riccati equations; Energy-optimal control; Jump-driven Ornstein-Uhlenbeck process; Riccati equation subject to a singular terminal condition;

D O I：

10.1109/LCSYS.2023.3271422

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We study a version of the Ornstein-Uhlenbeck bridge driven by a spectrally-positive subordinator. Our formulation is based on a Linear-Quadratic control subject to a singular terminal condition. The Ornstein-Uhlenbeck bridge, we develop, is written as a limit of the obtained optimally controlled processes, and is shown to admit an explicit expression. Its extension with self-excitement is also considered. The terminal condition is confirmed to be satisfied by the obtained process both analytically and numerically. The methods are also applied to a streamflow regulation problem using a real-life dataset.

引用

页码：1536 / 1541

页数：6