Equivalent cost functionals and stochastic linear quadratic optimal control problems

Zhiyong Yu

ESAIM: Control, Optimisation and Calculus of Variations (2013)

  • Volume: 19, Issue: 1, page 78-90
  • ISSN: 1292-8119

Abstract

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This paper is concerned with the stochastic linear quadratic optimal control problems (LQ problems, for short) for which the coefficients are allowed to be random and the cost functionals are allowed to have negative weights on the square of control variables. We propose a new method, the equivalent cost functional method, to deal with the LQ problems. Comparing to the classical methods, the new method is simple, flexible and non-abstract. The new method can also be applied to deal with nonlinear optimization problems.

How to cite

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Yu, Zhiyong. "Equivalent cost functionals and stochastic linear quadratic optimal control problems." ESAIM: Control, Optimisation and Calculus of Variations 19.1 (2013): 78-90. <http://eudml.org/doc/272809>.

@article{Yu2013,
abstract = {This paper is concerned with the stochastic linear quadratic optimal control problems (LQ problems, for short) for which the coefficients are allowed to be random and the cost functionals are allowed to have negative weights on the square of control variables. We propose a new method, the equivalent cost functional method, to deal with the LQ problems. Comparing to the classical methods, the new method is simple, flexible and non-abstract. The new method can also be applied to deal with nonlinear optimization problems.},
author = {Yu, Zhiyong},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
keywords = {stochastic LQ problem; stochastic hamiltonian system; forward-backward stochastic differential equation; Riccati equation; stochastic maximum principle; stochastic linear quadratic (LQ) problem; stochastic Hamiltonian system},
language = {eng},
number = {1},
pages = {78-90},
publisher = {EDP-Sciences},
title = {Equivalent cost functionals and stochastic linear quadratic optimal control problems},
url = {http://eudml.org/doc/272809},
volume = {19},
year = {2013},
}

TY - JOUR
AU - Yu, Zhiyong
TI - Equivalent cost functionals and stochastic linear quadratic optimal control problems
JO - ESAIM: Control, Optimisation and Calculus of Variations
PY - 2013
PB - EDP-Sciences
VL - 19
IS - 1
SP - 78
EP - 90
AB - This paper is concerned with the stochastic linear quadratic optimal control problems (LQ problems, for short) for which the coefficients are allowed to be random and the cost functionals are allowed to have negative weights on the square of control variables. We propose a new method, the equivalent cost functional method, to deal with the LQ problems. Comparing to the classical methods, the new method is simple, flexible and non-abstract. The new method can also be applied to deal with nonlinear optimization problems.
LA - eng
KW - stochastic LQ problem; stochastic hamiltonian system; forward-backward stochastic differential equation; Riccati equation; stochastic maximum principle; stochastic linear quadratic (LQ) problem; stochastic Hamiltonian system
UR - http://eudml.org/doc/272809
ER -

References

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