Optimistic value based optimal control for uncertain linear singular systems and application to a dynamic input-output model
In this paper, optimal control problems for uncertain discrete-time singular systems and uncertain continuous-time singular systems are considered under optimistic value criterion. The above singular systems are assumed to be regular and impulse-free, and optimistic value method is employed to optim...
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| Published in | ISA transactions Vol. 71; no. Pt 2; pp. 235 - 251 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
United States
Elsevier Ltd
01.11.2017
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| Online Access | Get full text |
| ISSN | 0019-0578 1879-2022 1879-2022 |
| DOI | 10.1016/j.isatra.2017.08.007 |
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| Abstract | In this paper, optimal control problems for uncertain discrete-time singular systems and uncertain continuous-time singular systems are considered under optimistic value criterion. The above singular systems are assumed to be regular and impulse-free, and optimistic value method is employed to optimize uncertain objective functions. Firstly, based on Bellman's principle of optimality, a recurrence equation is presented for settling optimal control problems subject to uncertain discrete-time singular systems. Then, by applying the principle of optimality and uncertainty theory, an equation of optimality for an optimal control model subject to an uncertain continuous-time singular system is derived. The optimal control problem can be settled through solving the equation of optimality. Two numerical examples and a dynamic input-output model are given to show the effectiveness of the results obtained.
•Optimal control problems subject to uncertain discrete-time (and continuous-time) singular systems are considered under optimistic value criterion.•Employing Bellman’s principle of optimality, a recurrence equation is presented to study uncertain discrete-time optimal control models.•The corresponding optimal controls are bang-bang provided that the objective function is linear in an uncertain discrete-time optimal control problem.•An equation of optimality is derived to solve optimal control problems for uncertain continuous-time singular systems if the input vector is derivable.•A dynamic input-output model is investigated as an application to illustrate the results obtained. |
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| AbstractList | In this paper, optimal control problems for uncertain discrete-time singular systems and uncertain continuous-time singular systems are considered under optimistic value criterion. The above singular systems are assumed to be regular and impulse-free, and optimistic value method is employed to optimize uncertain objective functions. Firstly, based on Bellman's principle of optimality, a recurrence equation is presented for settling optimal control problems subject to uncertain discrete-time singular systems. Then, by applying the principle of optimality and uncertainty theory, an equation of optimality for an optimal control model subject to an uncertain continuous-time singular system is derived. The optimal control problem can be settled through solving the equation of optimality. Two numerical examples and a dynamic input-output model are given to show the effectiveness of the results obtained. In this paper, optimal control problems for uncertain discrete-time singular systems and uncertain continuous-time singular systems are considered under optimistic value criterion. The above singular systems are assumed to be regular and impulse-free, and optimistic value method is employed to optimize uncertain objective functions. Firstly, based on Bellman's principle of optimality, a recurrence equation is presented for settling optimal control problems subject to uncertain discrete-time singular systems. Then, by applying the principle of optimality and uncertainty theory, an equation of optimality for an optimal control model subject to an uncertain continuous-time singular system is derived. The optimal control problem can be settled through solving the equation of optimality. Two numerical examples and a dynamic input-output model are given to show the effectiveness of the results obtained. •Optimal control problems subject to uncertain discrete-time (and continuous-time) singular systems are considered under optimistic value criterion.•Employing Bellman’s principle of optimality, a recurrence equation is presented to study uncertain discrete-time optimal control models.•The corresponding optimal controls are bang-bang provided that the objective function is linear in an uncertain discrete-time optimal control problem.•An equation of optimality is derived to solve optimal control problems for uncertain continuous-time singular systems if the input vector is derivable.•A dynamic input-output model is investigated as an application to illustrate the results obtained. In this paper, optimal control problems for uncertain discrete-time singular systems and uncertain continuous-time singular systems are considered under optimistic value criterion. The above singular systems are assumed to be regular and impulse-free, and optimistic value method is employed to optimize uncertain objective functions. Firstly, based on Bellman's principle of optimality, a recurrence equation is presented for settling optimal control problems subject to uncertain discrete-time singular systems. Then, by applying the principle of optimality and uncertainty theory, an equation of optimality for an optimal control model subject to an uncertain continuous-time singular system is derived. The optimal control problem can be settled through solving the equation of optimality. Two numerical examples and a dynamic input-output model are given to show the effectiveness of the results obtained.In this paper, optimal control problems for uncertain discrete-time singular systems and uncertain continuous-time singular systems are considered under optimistic value criterion. The above singular systems are assumed to be regular and impulse-free, and optimistic value method is employed to optimize uncertain objective functions. Firstly, based on Bellman's principle of optimality, a recurrence equation is presented for settling optimal control problems subject to uncertain discrete-time singular systems. Then, by applying the principle of optimality and uncertainty theory, an equation of optimality for an optimal control model subject to an uncertain continuous-time singular system is derived. The optimal control problem can be settled through solving the equation of optimality. Two numerical examples and a dynamic input-output model are given to show the effectiveness of the results obtained. |
| Author | Shu, Yadong Zhu, Yuanguo |
| Author_xml | – sequence: 1 givenname: Yadong surname: Shu fullname: Shu, Yadong email: 972718523@qq.com – sequence: 2 givenname: Yuanguo surname: Zhu fullname: Zhu, Yuanguo email: adamsue17@gmail.com |
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| Cites_doi | 10.1080/01969722.2012.707574 10.1016/j.aml.2014.07.002 10.1016/0022-0531(71)90038-X 10.1007/s10700-010-9073-2 10.1137/0327063 10.1016/j.isatra.2015.12.019 10.1016/S0005-1098(96)00193-8 10.1142/S0218488513400060 10.1080/01969722.2010.511552 10.1016/j.isatra.2014.08.010 10.2143/AST.30.1.504625 10.1016/j.aml.2014.07.003 10.1109/TSMC.1979.4310229 10.1007/s00500-012-0928-z 10.1007/s10700-015-9210-z |
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| Keywords | Equation of optimality Recurrence equation Optimistic value Optimal control Uncertain singular system |
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