Hostname: page-component-6bf8c574d5-gr6zb Total loading time: 0 Render date: 2025-02-17T12:02:47.190Z Has data issue: false hasContentIssue false
  • English
  • Français

Risk-sensitive linear/quadratic/gaussian control

Published online by Cambridge University Press:  01 July 2016

P. Whittle
P. Whittle*
Affiliation:
University of Cambridge
*
∗Postal address: Statistical Laboratory, University of Cambridge, 16 Mill Lane, Cambridge CB2 1SB, U.K.
Get access Rights & Permissions [Opens in a new window]

Abstract

The conventional linear/quadratic/Gaussian assumptions are modified in that minimisation of the expectation of cost G defined by (2) is replaced by minimisation of the criterion function (5). The scalar –θ is a measure of risk-aversion. It is shown that modified versions of certainty equivalence and the separation theorem still hold, that optimal control is still linear Markov, and state estimate generated by a version of the Kalman filter. There are also various new features, remarked upon in Sections 5 and 7. The paper generalises earlier work of Jacobson.

Keywords

LINEAR/QUADRATIC CONTROLRISK-SENSITIVITYCERTAINTY EQUIVALENCEKALMAN FILTER
Type
Research Article
Information
Advances in Applied Probability , Volume 13 , Issue 4 , December 1981 , pp. 764 - 777
Copyright
Copyright © Applied Probability Trust 1981 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

References

Bertsekas, D. P. (1976) Dynamic Programming and Stochastic Control. Academic Press, New York.Google Scholar
Davis, M. H. A. (1977) Linear Estimation and Stochastic Control. Chapman and Hall, London.Google Scholar
DeGroot, M. (1970) Optimal Statistical Decisions. McGraw-Hill, New York.Google Scholar
Howard, R. and Matheson, J. (1972) Risk-sensitive Markov decision processes. Management Sci. 18, 356–369.CrossRefGoogle Scholar
Jacobson, D. H. (1973) Optimal stochastic linear systems with exponential performance criteria and their relation to deterministic differential games. IEEE Trans. Automatic Control AC-18, 124–131.CrossRefGoogle Scholar
Jacobson, D. H. (1977) Extensions of Linear-Quadratic Control, Optimization and Matrix Theory. Academic Press, New York.Google Scholar
Kreps, D. M. (1972) Decision problems with expected utility criteria. I: Upper and lower convergent utility. Math. Operat. Res. 2, 45–53.CrossRefGoogle Scholar
Kushner, H. (1971) Introduction to Stochastic Control. Holt, Rinehart and Winston, New York.Google Scholar
Whittle, P. (1963) Prediction and Regulation. English Universities Press, London.Google Scholar
Whittle, P. (1971) Optimisation Under Constraints. Wiley Interscience, London.Google Scholar
Whittle, P. (1982) Optimisation Over Time. Wiley Interscience, London.Google Scholar

Additional references

Kumar, P. R. and Van Schuppen, J. H. (1981) On the optimal control of stochastic systems with an exponential-of-integral performance index. J. Math. Anal. Appl. 80, 312–332.CrossRefGoogle Scholar
Speyer, J. L. (1976) An adaptive terminal guidance scheme based on an exponential cost criterion with application to homing missile guidance. IEEE Trans. Automatic Control AC-21, 371–375.CrossRefGoogle Scholar
Speyer, J. L., Deyst, J. and Jacobson, D. H. (1974) Optimisation of stochastic linear systems with additive measurement and process noise using exponential performance criteria. IEEE Trans. Automatic Control AC-19, 358–366.CrossRefGoogle Scholar