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Information-theoretic approach to the study of control systems

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  • Touchette, Hugo
  • Lloyd, Seth

Abstract

We propose an information-theoretic framework for analyzing control systems based on the close relationship of controllers to communication channels. A communication channel takes an input state and transforms it into an output state. A controller, similarly, takes the initial state of a system to be controlled and transforms it into a target state. In this sense, a controller can be thought of as an actuation channel that acts on inputs to produce desired outputs. In this transformation process, two different control strategies can be adopted: (i) the controller applies an actuation dynamics that is independent of the state of the system to be controlled (open-loop control); or (ii) the controller enacts an actuation dynamics that is based on some information about the state of the controlled system (closed-loop control). Using this communication channel model of control, we provide necessary and sufficient conditions for a system to be perfectly controllable and perfectly observable in terms of information and entropy. In addition, we derive a quantitative trade-off between the amount of information gathered by a closed-loop controller and its relative performance advantage over an open-loop controller in stabilizing a system. This work supplements earlier results (Phys. Rev. Lett. 84 (2000) 1156) by providing new derivations of the advantage afforded by closed-loop control and by proposing an information-based optimality criterion for control systems. New applications of this approach pertaining to proportional controllers, and the control of chaotic maps are also presented.

Suggested Citation

  • Touchette, Hugo & Lloyd, Seth, 2004. "Information-theoretic approach to the study of control systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 331(1), pages 140-172.
    • Handle: RePEc:eee:phsmap:v:331:y:2004:i:1:p:140-172
    DOI: 10.1016/j.physa.2003.09.007
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    Cited by:

    1. E. M. S. Ribeiro & G. A. Prataviera, 2014. "Information theoretic approach for accounting classification," Papers 1401.2954, arXiv.org, revised Sep 2014.
    2. Ribeiro, E.M.S. & Prataviera, G.A., 2014. "Information theoretic approach for accounting classification," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 651-660.
    3. Igor Lazov, 2016. "A methodology for information and capacity analysis of broadband wireless access systems," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 63(2), pages 127-139, October.
    4. Lazov, Igor, 2017. "Profit management of car rental companies," European Journal of Operational Research, Elsevier, vol. 258(1), pages 307-314.
    5. Lazov, Petar & Lazov, Igor, 2014. "A general methodology for population analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 415(C), pages 557-594.

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