Optimal Vibration Control of a Class of Nonlinear Stochastic Systems with Markovian Jump
The semi-infinite time optimal control for a class of stochastically excited Markovian jump nonlinear system is investigated. Using stochastic averaging, each form of the system is reduced to a one-dimensional partially averaged Itô equation of total energy. A finite set of coupled dynamical program...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Shock and Vibration |
| Online Access: | http://dx.doi.org/10.1155/2016/9641075 |
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| _version_ | 1849690059665571840 |
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| author | R. H. Huan R. C. Hu D. Pu W. Q. Zhu |
| author_facet | R. H. Huan R. C. Hu D. Pu W. Q. Zhu |
| author_sort | R. H. Huan |
| collection | DOAJ |
| description | The semi-infinite time optimal control for a class of stochastically excited Markovian jump nonlinear system is investigated. Using stochastic averaging, each form of the system is reduced to a one-dimensional partially averaged Itô equation of total energy. A finite set of coupled dynamical programming equations is then set up based on the stochastic dynamical programming principle and Markovian jump rules, from which the optimal control force is obtained. The stationary response of the optimally controlled system is predicted by solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged Itô equation. Two examples are worked out in detail to illustrate the application and effectiveness of the proposed control strategy. |
| format | Article |
| id | doaj-art-ece30fafab104842a5640fa59709b919 |
| institution | DOAJ |
| issn | 1070-9622 1875-9203 |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Shock and Vibration |
| spelling | doaj-art-ece30fafab104842a5640fa59709b9192025-08-20T03:21:26ZengWileyShock and Vibration1070-96221875-92032016-01-01201610.1155/2016/96410759641075Optimal Vibration Control of a Class of Nonlinear Stochastic Systems with Markovian JumpR. H. Huan0R. C. Hu1D. Pu2W. Q. Zhu3Department of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, ChinaDepartment of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, ChinaDepartment of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, ChinaDepartment of Mechanics, State Key Laboratory of Fluid Power Transmission and Control, Zhejiang University, Hangzhou 310027, ChinaThe semi-infinite time optimal control for a class of stochastically excited Markovian jump nonlinear system is investigated. Using stochastic averaging, each form of the system is reduced to a one-dimensional partially averaged Itô equation of total energy. A finite set of coupled dynamical programming equations is then set up based on the stochastic dynamical programming principle and Markovian jump rules, from which the optimal control force is obtained. The stationary response of the optimally controlled system is predicted by solving the Fokker-Planck-Kolmogorov (FPK) equation associated with the fully averaged Itô equation. Two examples are worked out in detail to illustrate the application and effectiveness of the proposed control strategy.http://dx.doi.org/10.1155/2016/9641075 |
| spellingShingle | R. H. Huan R. C. Hu D. Pu W. Q. Zhu Optimal Vibration Control of a Class of Nonlinear Stochastic Systems with Markovian Jump Shock and Vibration |
| title | Optimal Vibration Control of a Class of Nonlinear Stochastic Systems with Markovian Jump |
| title_full | Optimal Vibration Control of a Class of Nonlinear Stochastic Systems with Markovian Jump |
| title_fullStr | Optimal Vibration Control of a Class of Nonlinear Stochastic Systems with Markovian Jump |
| title_full_unstemmed | Optimal Vibration Control of a Class of Nonlinear Stochastic Systems with Markovian Jump |
| title_short | Optimal Vibration Control of a Class of Nonlinear Stochastic Systems with Markovian Jump |
| title_sort | optimal vibration control of a class of nonlinear stochastic systems with markovian jump |
| url | http://dx.doi.org/10.1155/2016/9641075 |
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