Value of Information in Feedback Control: Global Optimality

The 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 m...

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Vydané v:IEEE transactions on automatic control Ročník 68; číslo 6; s. 3641 - 3647
Hlavní autori: Soleymani, Touraj, Baras, John S., Hirche, Sandra, Johansson, Karl H.
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York IEEE 01.06.2023
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Predmet:
Costs
Decision policies
Decision policy
Estimation
Feedback control
Gaussian process
Global optimality
Globally optimal solution
globally optimal solutions
Markov processes
Network control
networked control systems
Optimal control
Optimal controls
Optimal solutions
Optimal systems
Optimization
Process control
Quantization (signal)
rate-regulation tradeoff
Semantic communication
semantic communications
semantic metrics
Semantics
Tradeoffs
value of information
ISSN:0018-9286, 1558-2523, 1558-2523
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Shrnutí:The 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 <inline-formula><tex-math notation="LaTeX">\mathbf{{VoI}}_{{\boldsymbol{k}}}</tex-math></inline-formula>, 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 <inline-formula><tex-math notation="LaTeX">{\boldsymbol{k}}</tex-math></inline-formula> be transmitted to the controller only if <inline-formula><tex-math notation="LaTeX">\mathbf{{VoI}}_{{\boldsymbol{k}}}</tex-math></inline-formula> becomes nonnegative. These findings have important implications in the areas of communication and control.
Bibliografia:ObjectType-Article-1
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content type line 14
ISSN:0018-9286
1558-2523
1558-2523
DOI:10.1109/TAC.2022.3194125