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Information and control: Witsenhausen revisited

  • Sanjoy Mitter
  • Anant Sahai
Part C Modeling, Identification And Estimation
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 241)

Abstract

The role of information in the context of control is a deep issue. To get at this, we review Witsenhausen’s notions of information patterns for control problems. While staying in that basic framework, we then use ideas from traditional information theory as we re-examine Witsenhausen’s famous “counterexample”. In the process, we construct a family of nonlinear “quantizing” control laws that can perform infinitely better than the best linear policies.

Keywords

Conditional Distribution Gaussian Random Variable Quadratic Cost Stochastic Optimum Control Nonlinear Controller 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    Anant Sahai. Sending 1 signal over 2 channels. Unpublished Work, 1998.Google Scholar
  2. [2]
    Sekhar Tatikonda, Anant Sahai, and Sanjoy Mitter. LQG control under communication constraints. Submitted to the 1998 CDC.Google Scholar
  3. [3]
    H. S. Witsenhausen. A counterexample in stochastic optimum control. SIAM Journal of Control, 6(1):131–147, 1968.zbMATHCrossRefMathSciNetGoogle Scholar
  4. [4]
    H. S. Witsenhausen. Separation of estimation and control for discrete time systems. Proceedings of the IEEE, 59(11):1557–1566, 1971.MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag London Limited 1999

Authors and Affiliations

  • Sanjoy Mitter
  • Anant Sahai
    • 1
  1. 1.Department of Electrical Engineering and Computer Science and Laboratory for Information and Decision SystemsMassachusetts Institute of TechnologyUSA

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