Optimal Covariance Steering for Discrete-Time Linear Stochastic Systems

• 成果类型: Article
• 署名作者: Liu, Fengjiao; Rapakoulias, George; Tsiotras, Panagiotis
• 署名单位: State University System of Florida; Florida A&M University; Florida State University; 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.2024.3472788
• 发表日期: 2025
• 页码: 2289-2304
• 关键词: Optimal control; Difference equations; Sufficient conditions; Stochastic systems; Space vehicles; Convex functions; Trajectory optimization; State feedback; PROCESS CONTROL; Probabilistic logic; Covariance steering; Riccati difference equation; semidefinite program (SDP)

摘要

In this article, we study the optimal control problem for steering the state covariance of a discrete-time linear stochastic system over a finite time horizon. First, we establish the existence and uniqueness of the optimal control law for a quadratic cost function. Then, we show the separation of the optimal mean and the covariance steering problems. We also develop efficient computational methods to solve for the optimal control law, which is identified as the solution to a semidefinite program. The effectiveness of the proposed approach is demonstrated through numerical examples. In the process, we also obtain some novel theoretical results for a matrix Riccati difference equation, which may be of independent interest.