Optimal Covariance Steering for Continuous-Time Linear Stochastic Systems With Martingale Additive Noise

• 成果类型: Article
• 署名作者: Liu, Fengjiao; Tsiotras, Panagiotis
• 署名单位: University System of Georgia; Georgia Institute of Technology
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2023.3331683
• 发表日期: 2024
• 页码: 2591-2597
• 关键词: Controllability; optimal control; Covariance matrices; Stochastic systems; Time-varying systems; Stochastic processes; State feedback; Additive noise; Covariance steering; finite horizon; Riccati differential equation; stochastic control

摘要

In this article, we study the problem of how to optimally steer the state covariance of a general continuous-time linear stochastic system over a finite time interval subject to additive noise. Optimality here means reaching a target state covariance with minimal control energy. The additive noise may include a combination of white Gaussian noise and abrupt jump noise that is discontinuous in time. We first establish the controllability of the state covariance for linear time-varying stochastic systems. We then derive the optimal control, which entails solving two coupled matrix ordinary differential equations (ODEs) with split boundary conditions. We show the existence and uniqueness of the solution to these coupled matrix ODEs, and thus those of the optimal control.