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Optimal control of stochastic Ito differential systems by fixed terminal time

Published online by Cambridge University Press:  01 July 2016

N. U. Ahmed  and
K. L. Teo
N. U. Ahmed
Affiliation:
University of Ottawa
K. L. Teo
Affiliation:
University of New South Wales
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Abstract

In this paper, the authors consider a class of stochastic systems described by Ito differential equations for which both controls and parameters are to be chosen optimally with respect to a certain performance index over a fixed time interval. The controls to be optimized depend only on partially observed current states as in a work of Fleming. However, he considered, instead, a problem of optimal control of systems governed by stochastic Ito differential equations with Markov terminal time. The fixed time problems usually give rise to the Cauchy problems (unbounded domain) whereas the Markov time problems give rise to the first boundary value problems (bounded domain). This fact makes the former problems relatively more involved than the latter. For the latter problems, Fleming has reported a necessary condition for optimality and an existence theorem of optimal controls. In this paper, a necessary condition for optimality for both controls and parameters combined together is presented for the former problems.

Keywords

STOCHASTIC ITO DIFFERENTIAL EQUATIONSFIXED TERMINAL TIMENECESSARY CONDITION FOR OPTIMALITYOPTIMAL CONTROLSOPTIMAL PARAMETERSPARTIAL DIFFERENTIAL EQUATIONPARABOLIC TYPECAUCHY CONDITION
Type
Research Article
Information
Advances in Applied Probability , Volume 7 , Issue 1 , March 1975 , pp. 154 - 178
Copyright
Copyright © Applied Probability Trust 1975 

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References

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