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Information-theoretic limits of control

Touchette1, Lloyd

  • 1d'Arbeloff Laboratory for Information Systems and Technology, Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.

Physical Review Letters
|October 4, 2000
PubMed
Summary
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Information theory reveals fundamental limits on controlling physical systems. The generalized second law of thermodynamics dictates minimum energy dissipation for open-loop control, while feedback control offers limited entropy reduction per bit of information.

Area of Science:

  • Thermodynamics
  • Information Theory
  • Control Systems Engineering

Background:

  • Understanding the fundamental limits of physical system control is crucial for advancements in engineering and science.
  • The interplay between thermodynamics and information theory has profound implications for system controllability.

Purpose of the Study:

  • To explore the theoretical boundaries on the controllability of physical systems using information theory.
  • To investigate the role of the generalized second law of thermodynamics in setting limits on control system dissipation.
  • To analyze the efficacy of feedback control in reducing system entropy from an information-theoretic perspective.

Main Methods:

  • Application of information theory principles to analyze control system dynamics.

Related Experiment Videos

  • Generalization of the second law of thermodynamics to incorporate information.
  • Information-theoretic analysis of open-loop and feedback control strategies.
  • Main Results:

    • The generalized second law of thermodynamics establishes absolute minimum dissipation requirements for open-loop control.
    • Feedback control is characterized as a zero-sum game; each acquired bit of information yields at most one bit of additional entropy reduction.
    • The study discusses implications for controlling discrete state systems and chaotic maps.

    Conclusions:

    • Information theory provides a framework for understanding the fundamental limits of physical system control.
    • Thermodynamic constraints, when considering information, are essential for defining control system performance.
    • The analysis highlights the inherent trade-offs and limitations in entropy reduction through feedback control.