Value of Information in Feedback Control: Global Optimality

• 成果类型: Article
• 署名作者: Soleymani, Touraj; Baras, John S.; Hirche, Sandra; Johansson, Karl H.
• 署名单位: Royal Institute of Technology; University System of Maryland; University of Maryland College Park; Technical University of Munich
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2022.3194125
• 发表日期: 2023
• 页码: 3641-3647
• 关键词: estimation; PROCESS CONTROL; Markov processes; semantics; optimal control; Quantization (signal); COSTS; Decision policies; globally optimal solutions; networked control systems; rate-regulation tradeoff; semantic communications; semantic metrics; value of information

摘要

rate-regulation tradeoff, defined between two objective functions, one penalizing the packet rate and one the regulation cost, can express the fundamental performance bound of networked control systems. However, the characterization of the set of globally optimal solutions in this tradeoff for multidimensional Gauss-Markov processes has been an open problem. In this article, we characterize a policy profile that belongs to this set without imposing any restrictions on the information structure or the policy structure. We prove that such a policy profile consists of a symmetric threshold triggering policy based on the value of information and a certainty-equivalent control policy based on a non-Gaussian linear estimator. These policies are deterministic and can be designed separately. Besides, we provide a global optimality analysis for the value of information VoI(k), a semantic metric that emerges from the rate-regulation tradeoff as the difference between the benefit and the cost of a data packet. We prove that it is globally optimal that a data packet containing sensory information at time k be transmitted to the controller only if VoI(k) becomes nonnegative. These findings have important implications in the areas of communication and control.