Study on Stochastic Linear Quadratic Optimal Control with Quadratic and Mixed Terminal State Constraints
This paper studies the indefinite stochastic LQ control problem with quadratic and mixed terminal state equality constraints, which can be transformed into a mathematical programming problem. By means of the Lagrangian multiplier theorem and Riesz representation theorem, the main result given in thi...
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/674327 |
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| _version_ | 1832556632280662016 |
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| author | Yang Hongli |
| author_facet | Yang Hongli |
| author_sort | Yang Hongli |
| collection | DOAJ |
| description | This paper studies the indefinite stochastic LQ control problem
with quadratic and mixed terminal state equality constraints, which can
be transformed into a mathematical programming problem. By means
of the Lagrangian multiplier theorem and Riesz representation theorem, the
main result given in this paper is the necessary condition for indefinite
stochastic LQ control with quadratic and mixed terminal equality
constraints. The result shows that the different terminal state constraints
will cause the endpoint condition of the differential Riccati equation
to be changed. It coincides with the indefinite stochastic LQ problem
with linear terminal state constraint, so the result given in this paper can
be viewed as the extension of the indefinite stochastic LQ problem
with the linear terminal state equality constraint. In order to guarantee
the existence and the uniqueness of the linear feedback control, a
sufficient condition is also presented in the paper. A numerical example
is presented at the end of the paper. |
| format | Article |
| id | doaj-art-b2ac3948cea643658c6e2eaf0b821989 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-b2ac3948cea643658c6e2eaf0b8219892025-02-03T05:44:46ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/674327674327Study on Stochastic Linear Quadratic Optimal Control with Quadratic and Mixed Terminal State ConstraintsYang Hongli0Information and Electrical Engineering College, Shandong University of Science and Technology, Qingdao, Shandong 266590, ChinaThis paper studies the indefinite stochastic LQ control problem with quadratic and mixed terminal state equality constraints, which can be transformed into a mathematical programming problem. By means of the Lagrangian multiplier theorem and Riesz representation theorem, the main result given in this paper is the necessary condition for indefinite stochastic LQ control with quadratic and mixed terminal equality constraints. The result shows that the different terminal state constraints will cause the endpoint condition of the differential Riccati equation to be changed. It coincides with the indefinite stochastic LQ problem with linear terminal state constraint, so the result given in this paper can be viewed as the extension of the indefinite stochastic LQ problem with the linear terminal state equality constraint. In order to guarantee the existence and the uniqueness of the linear feedback control, a sufficient condition is also presented in the paper. A numerical example is presented at the end of the paper.http://dx.doi.org/10.1155/2013/674327 |
| spellingShingle | Yang Hongli Study on Stochastic Linear Quadratic Optimal Control with Quadratic and Mixed Terminal State Constraints Journal of Applied Mathematics |
| title | Study on Stochastic Linear Quadratic Optimal Control with Quadratic and Mixed Terminal State Constraints |
| title_full | Study on Stochastic Linear Quadratic Optimal Control with Quadratic and Mixed Terminal State Constraints |
| title_fullStr | Study on Stochastic Linear Quadratic Optimal Control with Quadratic and Mixed Terminal State Constraints |
| title_full_unstemmed | Study on Stochastic Linear Quadratic Optimal Control with Quadratic and Mixed Terminal State Constraints |
| title_short | Study on Stochastic Linear Quadratic Optimal Control with Quadratic and Mixed Terminal State Constraints |
| title_sort | study on stochastic linear quadratic optimal control with quadratic and mixed terminal state constraints |
| url | http://dx.doi.org/10.1155/2013/674327 |
| work_keys_str_mv | AT yanghongli studyonstochasticlinearquadraticoptimalcontrolwithquadraticandmixedterminalstateconstraints |