Abstract
Control and filtering of decentralized systems can benefit from a decomposition of the available observations into components. The concepts of common, private, correlated, and sufficient information have been proposed and are defined in this chapter. A decentralized control system in which the outputs and the states have been decomposed with respect to these concepts will facilitate the synthesis of communication laws and control laws for decentralized control.
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References
Hexner G, Ho YC (1977) Information structure: common and private. IEEE Trans Inf Theor 23:390–393
Ho YC, Hexner G, Martin C (1976) Two person information structure. Part I: information structure: common and private. Part II: private information structures of A with respect to B. Report 663, Division of Engineering and Applied Physics, Harvard University, Cambridge, MA, USA, July 1976
Wyner AD (1975) The common information of two dependent random variables. IEEE Trans Inf Theor 21:163–179
Wyner AD (1978) A definition of conditional mutual information for arbitrary ensembles. Inf Control 38:51–59
van Schuppen JH (1982) The strong finite stochastic realization problem—Preliminary results. In: Bensoussan A, Lions JL (eds) Analysis and optimization of systems, vol 44., Lecture Notes in Control and Information SciencesSpringer, Berlin, pp 179–190
van Schuppen JH (2000) Stochastic realization of \(\sigma \)-algebras. In: Proceedings of 14th international symposium MTNS (published on CD-ROM only), Université de Perpignan, Perpignan
Ho YC (1980) Team decision theory and information structures. Proc IEEE 68:644–654
Ho YC, Karstner P, Wong E (1978) Teams, signaling and information theory. IEEE Trans Autom Control 23:305–311
Dick R, Hexner G, Ho Y (1977) On common information in decision problems. IEEE Trans Inf Theor 23:393–396
Aumann RJ (1976) Agreeing to disagree. Ann Statist 4:1236–1239
Hotelling H (1936) Relation between two sets of variates. Biometrika 28:321–377
Gittens RD (1985) Canonical analysis—A review with applications in ecology. Springer, Berlin
van Putten C, van Schuppen JH (1983) The weak and strong Gaussian probabilistic realization problem. J Multivariate Anal 13:118–137
Wonham WM (1979) Linear multivariable control: a geometric approach. Springer, Berlin
Kempker PL, Ran A, van Schuppen JH (2012) Controllability and observability of coordinated linear systems. Linear Algebra its Appl 437:121–167
Cover TM, Thomas JA (1991) Elements of information theory. Wiley, New York
Gallager RG (1968) Information theory and reliable communication. Wiley, New York
Ihara S (1993) Information theory for continuous systems. World Scientific, Singapore
Witsenhausen HS (1976) Some remarks on the concept of state. In: Directions in large-scale systems, many-person optimization, and decentralized control (Proceedings Symposium, Wakefield, MA, 1975), Plenum, New York, pp 69–75
Teneketzis D, Varaiya P (1984) Consensus in distributed estimation with inconsistent beliefs. Syst Control Lett 4:217–221
Washburn RB, Teneketzis D (1984) Asymptotic agreement among communicating decisionmakers. Stochastics 13:103–129
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van Schuppen, J.H. (2015). Common, Correlated, and Private Information in Control of Decentralized Systems. In: van Schuppen, J., Villa, T. (eds) Coordination Control of Distributed Systems. Lecture Notes in Control and Information Sciences, vol 456. Springer, Cham. https://doi.org/10.1007/978-3-319-10407-2_26
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DOI: https://doi.org/10.1007/978-3-319-10407-2_26
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