Feedback stabilization and adaptive stabilization of stochastic nonlinear systems by the control Lyapunov function
Our aims of this paper are twofold: On one hand, we study the asymptotic stability in probability of stochastic differential system, when both the drift and diffusion terms are affine in the control. We derive sufficient conditions for the existence of control Lyapunov functions (CLFs) leading to th...
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| Format: | Article |
| Language: | English |
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Taylor & Francis
2011
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| Online Access: | http://psasir.upm.edu.my/id/eprint/25052/ http://psasir.upm.edu.my/id/eprint/25052/1/Feedback%20stabilization%20and%20adaptive%20stabilization%20of%20stochastic%20nonlinear%20systems%20by%20the%20control%20Lyapunov%20function.pdf |
| _version_ | 1848845204695547904 |
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| author | Abedi, Fakhreddin Abu Hassan, Malik Suleiman, Mohamed |
| author_facet | Abedi, Fakhreddin Abu Hassan, Malik Suleiman, Mohamed |
| author_sort | Abedi, Fakhreddin |
| building | UPM Institutional Repository |
| collection | Online Access |
| description | Our aims of this paper are twofold: On one hand, we study the asymptotic stability in probability of stochastic differential system, when both the drift and diffusion terms are affine in the control. We derive sufficient conditions for the existence of control Lyapunov functions (CLFs) leading to the existence of stabilizing feedback laws which are smooth, except possibly at the equilibrium state. On the other hand, we consider the previous systems with an unknown constant parameters in the drift and introduce the concept of an adaptive CLF for stochastic system and use the stochastic version of Florchinger's control law to design an adaptive controller. In this framework, the problem of adaptive stabilization of nonlinear stochastic system is reduced to the problem of non-adaptive stabilization of a modified system. |
| first_indexed | 2025-11-15T08:43:06Z |
| format | Article |
| id | upm-25052 |
| institution | Universiti Putra Malaysia |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T08:43:06Z |
| publishDate | 2011 |
| publisher | Taylor & Francis |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | upm-250522018-10-18T07:41:54Z http://psasir.upm.edu.my/id/eprint/25052/ Feedback stabilization and adaptive stabilization of stochastic nonlinear systems by the control Lyapunov function Abedi, Fakhreddin Abu Hassan, Malik Suleiman, Mohamed Our aims of this paper are twofold: On one hand, we study the asymptotic stability in probability of stochastic differential system, when both the drift and diffusion terms are affine in the control. We derive sufficient conditions for the existence of control Lyapunov functions (CLFs) leading to the existence of stabilizing feedback laws which are smooth, except possibly at the equilibrium state. On the other hand, we consider the previous systems with an unknown constant parameters in the drift and introduce the concept of an adaptive CLF for stochastic system and use the stochastic version of Florchinger's control law to design an adaptive controller. In this framework, the problem of adaptive stabilization of nonlinear stochastic system is reduced to the problem of non-adaptive stabilization of a modified system. Taylor & Francis 2011 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/25052/1/Feedback%20stabilization%20and%20adaptive%20stabilization%20of%20stochastic%20nonlinear%20systems%20by%20the%20control%20Lyapunov%20function.pdf Abedi, Fakhreddin and Abu Hassan, Malik and Suleiman, Mohamed (2011) Feedback stabilization and adaptive stabilization of stochastic nonlinear systems by the control Lyapunov function. Stochastics, 83 (2). pp. 179-201. ISSN 1744-2508; ESSN: 1744-2516 https://www.tandfonline.com/doi/abs/10.1080/17442508.2011.552723?journalCode=gssr20 10.1080/17442508.2011.552723 |
| spellingShingle | Abedi, Fakhreddin Abu Hassan, Malik Suleiman, Mohamed Feedback stabilization and adaptive stabilization of stochastic nonlinear systems by the control Lyapunov function |
| title | Feedback stabilization and adaptive stabilization of stochastic nonlinear systems by the control Lyapunov function |
| title_full | Feedback stabilization and adaptive stabilization of stochastic nonlinear systems by the control Lyapunov function |
| title_fullStr | Feedback stabilization and adaptive stabilization of stochastic nonlinear systems by the control Lyapunov function |
| title_full_unstemmed | Feedback stabilization and adaptive stabilization of stochastic nonlinear systems by the control Lyapunov function |
| title_short | Feedback stabilization and adaptive stabilization of stochastic nonlinear systems by the control Lyapunov function |
| title_sort | feedback stabilization and adaptive stabilization of stochastic nonlinear systems by the control lyapunov function |
| url | http://psasir.upm.edu.my/id/eprint/25052/ http://psasir.upm.edu.my/id/eprint/25052/ http://psasir.upm.edu.my/id/eprint/25052/ http://psasir.upm.edu.my/id/eprint/25052/1/Feedback%20stabilization%20and%20adaptive%20stabilization%20of%20stochastic%20nonlinear%20systems%20by%20the%20control%20Lyapunov%20function.pdf |