A relaxation theorem for partially observed stochastic control on Hilbert space

N.U. Ahmed

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2007)

  • Volume: 27, Issue: 2, page 295-314
  • ISSN: 1509-9407

Abstract

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In this paper, we present a result on relaxability of partially observed control problems for infinite dimensional stochastic systems in a Hilbert space. This is motivated by the fact that measure valued controls, also known as relaxed controls, are difficult to construct practically and so one must inquire if it is possible to approximate the solutions corresponding to measure valued controls by those corresponding to ordinary controls. Our main result is the relaxation theorem which states that the set of solutions corresponding to ordinary controls is weakly dense in the set of solutions corresponding to relaxed controls. This is presented in Theorem 5.3 after giving some existence results on optimal controls for the infinite dimensional Zakai equation used for its proof.

How to cite

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N.U. Ahmed. "A relaxation theorem for partially observed stochastic control on Hilbert space." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 27.2 (2007): 295-314. <http://eudml.org/doc/271191>.

@article{N2007,
abstract = {In this paper, we present a result on relaxability of partially observed control problems for infinite dimensional stochastic systems in a Hilbert space. This is motivated by the fact that measure valued controls, also known as relaxed controls, are difficult to construct practically and so one must inquire if it is possible to approximate the solutions corresponding to measure valued controls by those corresponding to ordinary controls. Our main result is the relaxation theorem which states that the set of solutions corresponding to ordinary controls is weakly dense in the set of solutions corresponding to relaxed controls. This is presented in Theorem 5.3 after giving some existence results on optimal controls for the infinite dimensional Zakai equation used for its proof.},
author = {N.U. Ahmed},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {partially observed control; infinite dimensional Hilbert space; relaxed controls; Zakai equation},
language = {eng},
number = {2},
pages = {295-314},
title = {A relaxation theorem for partially observed stochastic control on Hilbert space},
url = {http://eudml.org/doc/271191},
volume = {27},
year = {2007},
}

TY - JOUR
AU - N.U. Ahmed
TI - A relaxation theorem for partially observed stochastic control on Hilbert space
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2007
VL - 27
IS - 2
SP - 295
EP - 314
AB - In this paper, we present a result on relaxability of partially observed control problems for infinite dimensional stochastic systems in a Hilbert space. This is motivated by the fact that measure valued controls, also known as relaxed controls, are difficult to construct practically and so one must inquire if it is possible to approximate the solutions corresponding to measure valued controls by those corresponding to ordinary controls. Our main result is the relaxation theorem which states that the set of solutions corresponding to ordinary controls is weakly dense in the set of solutions corresponding to relaxed controls. This is presented in Theorem 5.3 after giving some existence results on optimal controls for the infinite dimensional Zakai equation used for its proof.
LA - eng
KW - partially observed control; infinite dimensional Hilbert space; relaxed controls; Zakai equation
UR - http://eudml.org/doc/271191
ER -

References

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