Some New Results on Integral-Type Backstepping Method for a Control Problem Governed by a Linear Heat Equation
It is well known in the literature that the design of stabilization controllers for control systems governed by linear heat equations can be achieved by applying the integral-type backstepping transformation. In this paper, its focus is to establish three new results. First, by controllability theor...
| Main Authors: | , , |
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| Format: | Journal Article |
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Institute of Electrical and Electronics Engineers
2017
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| Online Access: | http://hdl.handle.net/20.500.11937/54787 |
| _version_ | 1848759460813602816 |
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| author | Zhou, Z. Yu, C. Teo, Kok Lay |
| author_facet | Zhou, Z. Yu, C. Teo, Kok Lay |
| author_sort | Zhou, Z. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | It is well known in the literature that the design of stabilization controllers for control systems governed by linear heat equations can be achieved by applying the integral-type backstepping transformation. In this paper, its focus is to establish three new results. First, by controllability theory, we show that the choice of kernels is unique in the context of integral-type backstepping transformation. Next, we show that the forward transformation and inverse transformation in the integral-type backstepping method are mutual transformation pair via solving an easily solvable PDE. With this result, the need of finding explicit solutions of kernel equations can be avoided. Finally, by constructing a corresponding LQ problem, we show that the optimal control of the LQ problem is exactly the stabilization control of the heat equation obtained by the integral-type backstepping method. |
| first_indexed | 2025-11-14T10:00:14Z |
| format | Journal Article |
| id | curtin-20.500.11937-54787 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T10:00:14Z |
| publishDate | 2017 |
| publisher | Institute of Electrical and Electronics Engineers |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-547872017-11-15T06:30:00Z Some New Results on Integral-Type Backstepping Method for a Control Problem Governed by a Linear Heat Equation Zhou, Z. Yu, C. Teo, Kok Lay It is well known in the literature that the design of stabilization controllers for control systems governed by linear heat equations can be achieved by applying the integral-type backstepping transformation. In this paper, its focus is to establish three new results. First, by controllability theory, we show that the choice of kernels is unique in the context of integral-type backstepping transformation. Next, we show that the forward transformation and inverse transformation in the integral-type backstepping method are mutual transformation pair via solving an easily solvable PDE. With this result, the need of finding explicit solutions of kernel equations can be avoided. Finally, by constructing a corresponding LQ problem, we show that the optimal control of the LQ problem is exactly the stabilization control of the heat equation obtained by the integral-type backstepping method. 2017 Journal Article http://hdl.handle.net/20.500.11937/54787 10.1109/TAC.2017.2671778 Institute of Electrical and Electronics Engineers restricted |
| spellingShingle | Zhou, Z. Yu, C. Teo, Kok Lay Some New Results on Integral-Type Backstepping Method for a Control Problem Governed by a Linear Heat Equation |
| title | Some New Results on Integral-Type Backstepping Method for a Control Problem Governed by a Linear Heat Equation |
| title_full | Some New Results on Integral-Type Backstepping Method for a Control Problem Governed by a Linear Heat Equation |
| title_fullStr | Some New Results on Integral-Type Backstepping Method for a Control Problem Governed by a Linear Heat Equation |
| title_full_unstemmed | Some New Results on Integral-Type Backstepping Method for a Control Problem Governed by a Linear Heat Equation |
| title_short | Some New Results on Integral-Type Backstepping Method for a Control Problem Governed by a Linear Heat Equation |
| title_sort | some new results on integral-type backstepping method for a control problem governed by a linear heat equation |
| url | http://hdl.handle.net/20.500.11937/54787 |