Risk-Aware Linear Quadratic Control Using Conditional Value-at-Risk

• 成果类型: Article
• 署名作者: Kishida, Masako; Cetinkaya, Ahmet
• 署名单位: Research Organization of Information & Systems (ROIS); National Institute of Informatics (NII) - Japan
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3142131
• 发表日期: 2023
• 页码: 416-423
• 关键词: Conditional-value-at-risk (CVaR); Linear systems; optimal control; stochastic optimal control

摘要

Stochastic linear quadratic control problems are considered from the viewpoint of risks. In particular, a worst-case conditional value-at-risk (CVaR) of quadratic objective function is minimized subject to additive disturbances whose first two moments of the distribution are known. The study focuses on three problems of finding the optimal feedback gain that minimizes the quadratic cost of: stationary distribution, one-step, and infinite time horizon. For the stationary distribution problem, it is proved that the optimal control gain that minimizes the worst-case CVaR of the quadratic cost is equivalent to that of the standard (stochastic) linear quadratic regulator. For the one-step problem, an approach to an optimal solution as well as analytical suboptimal solutions are presented. For the infinite time horizon problem, two suboptimal solutions that bound the optimal solution and an approach to an optimal solution for a special case are discussed. The presented theorems are illustrated with numerical examples.