Indefinite LQ Optimal Control with Terminal State Constraint for Discrete-Time Uncertain Systems
Uncertainty theory is a branch of mathematics for modeling human uncertainty based on the normality, duality, subadditivity, and product axioms. This paper studies a discrete-time LQ optimal control with terminal state constraint, whereas the weighting matrices in the cost function are indefinite an...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Journal of Control Science and Engineering |
| Online Access: | http://dx.doi.org/10.1155/2016/7241390 |
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| author | Yuefen Chen Minghai Yang |
| author_facet | Yuefen Chen Minghai Yang |
| author_sort | Yuefen Chen |
| collection | DOAJ |
| description | Uncertainty theory is a branch of mathematics for modeling human uncertainty based on the normality, duality, subadditivity, and product axioms. This paper studies a discrete-time LQ optimal control with terminal state constraint, whereas the weighting matrices in the cost function are indefinite and the system states are disturbed by uncertain noises. We first transform the uncertain LQ problem into an equivalent deterministic LQ problem. Then, the main result given in this paper is the necessary condition for the constrained indefinite LQ optimal control problem by means of the Lagrangian multiplier method. Moreover, in order to guarantee the well-posedness of the indefinite LQ problem and the existence of an optimal control, a sufficient condition is presented in the paper. Finally, a numerical example is presented at the end of the paper. |
| format | Article |
| id | doaj-art-d498a4c3eb09417f9088a020ee80b5d3 |
| institution | DOAJ |
| issn | 1687-5249 1687-5257 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Control Science and Engineering |
| spelling | doaj-art-d498a4c3eb09417f9088a020ee80b5d32025-08-20T03:23:46ZengWileyJournal of Control Science and Engineering1687-52491687-52572016-01-01201610.1155/2016/72413907241390Indefinite LQ Optimal Control with Terminal State Constraint for Discrete-Time Uncertain SystemsYuefen Chen0Minghai Yang1School of Science, Nanjing University of Science and Technology, Nanjing 210094, ChinaCollege of Mathematics and Information Science, Xinyang Normal University, Xinyang 464000, ChinaUncertainty theory is a branch of mathematics for modeling human uncertainty based on the normality, duality, subadditivity, and product axioms. This paper studies a discrete-time LQ optimal control with terminal state constraint, whereas the weighting matrices in the cost function are indefinite and the system states are disturbed by uncertain noises. We first transform the uncertain LQ problem into an equivalent deterministic LQ problem. Then, the main result given in this paper is the necessary condition for the constrained indefinite LQ optimal control problem by means of the Lagrangian multiplier method. Moreover, in order to guarantee the well-posedness of the indefinite LQ problem and the existence of an optimal control, a sufficient condition is presented in the paper. Finally, a numerical example is presented at the end of the paper.http://dx.doi.org/10.1155/2016/7241390 |
| spellingShingle | Yuefen Chen Minghai Yang Indefinite LQ Optimal Control with Terminal State Constraint for Discrete-Time Uncertain Systems Journal of Control Science and Engineering |
| title | Indefinite LQ Optimal Control with Terminal State Constraint for Discrete-Time Uncertain Systems |
| title_full | Indefinite LQ Optimal Control with Terminal State Constraint for Discrete-Time Uncertain Systems |
| title_fullStr | Indefinite LQ Optimal Control with Terminal State Constraint for Discrete-Time Uncertain Systems |
| title_full_unstemmed | Indefinite LQ Optimal Control with Terminal State Constraint for Discrete-Time Uncertain Systems |
| title_short | Indefinite LQ Optimal Control with Terminal State Constraint for Discrete-Time Uncertain Systems |
| title_sort | indefinite lq optimal control with terminal state constraint for discrete time uncertain systems |
| url | http://dx.doi.org/10.1155/2016/7241390 |
| work_keys_str_mv | AT yuefenchen indefinitelqoptimalcontrolwithterminalstateconstraintfordiscretetimeuncertainsystems AT minghaiyang indefinitelqoptimalcontrolwithterminalstateconstraintfordiscretetimeuncertainsystems |