Hostname: page-component-cd9895bd7-gxg78 Total loading time: 0 Render date: 2024-12-19T03:47:08.749Z Has data issue: false hasContentIssue false

The risk-sensitive certainty equivalence principle

Published online by Cambridge University Press:  14 July 2016

Abstract

A risk-sensitive certainty equivalence principle is deduced, expressed in Theorem 1, for a model with linear dynamics and observation rules, Gaussian noise and an exponential-quadratic criterion of the form (2). The senses in which one is now to understand certainty equivalence and the separation principle are discussed.

Type
Part 6—Allied Stochastic Processes
Copyright
Copyright © 1986 Applied Probability Trust 

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

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, 124131.Google Scholar
Jacobson, D. H. (1977) Extensions of Linear-Quadratic Control, Optimization and Matrix Theory. Academic Press, New York.Google Scholar
Theil, H. (1957) A note on certainty equivalence in dynamic planning. Econometrica 25, 346349.Google Scholar
Whittle, P. (1981) Risk-sensitive linear/quadratic Gaussian control. Adv. Appl. Prob. 13, 764777.Google Scholar
Whittle, P. (1982) Optimization over Time , Vol. 1. Wiley Interscience, New York.Google Scholar
Whittle, P. (1983) Prediction and Regulation by Linear Least Square Methods , 2nd edn. University of Minnesota Press, Minneapolis.Google Scholar
Whittle, P. and Kuhn, J. (1986) A Hamiltonian formulation of risk-sensitive linear/quadratic/Gaussian control. Int. J. Control. To appear.CrossRefGoogle Scholar