Global inverse optimal stabilization of stochastic nonholonomic systems
Optimality has not been addressed in existing works on control of (stochastic) nonholonomic systems.This paper presents a design of optimal controllers with respect to a meaningful cost function to globally asymptotically stabilize (in probability) nonholonomic systems affine in stochastic disturban...
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| Format: | Journal Article |
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Elsevier BV
2015
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| Online Access: | http://www.sciencedirect.com/science/article/pii/S0167691114002369 http://hdl.handle.net/20.500.11937/7294 |
| _version_ | 1848745328004562944 |
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| author | Do, Khac Duc |
| author_facet | Do, Khac Duc |
| author_sort | Do, Khac Duc |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Optimality has not been addressed in existing works on control of (stochastic) nonholonomic systems.This paper presents a design of optimal controllers with respect to a meaningful cost function to globally asymptotically stabilize (in probability) nonholonomic systems affine in stochastic disturbances. The design is based on the Lyapunov direct method, the backstepping technique, and the inverse optimal control design. A class of Lyapunov functions, which are not required to be as nonlinearly strong as quadratic or quartic, is proposed for the control design. Thus, these Lyapunov functions can be applied to design of controllers for underactuated (stochastic) mechanical systems, which are usually required Lyapunov functions of a nonlinearly weak form. The proposed control design is illustrated on a kinematic cart, of which wheel velocities are perturbed by stochastic noise. |
| first_indexed | 2025-11-14T06:15:36Z |
| format | Journal Article |
| id | curtin-20.500.11937-7294 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T06:15:36Z |
| publishDate | 2015 |
| publisher | Elsevier BV |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-72942019-02-19T04:26:27Z Global inverse optimal stabilization of stochastic nonholonomic systems Do, Khac Duc stochastic nonholonomic systems Lyapunov functions Optimality has not been addressed in existing works on control of (stochastic) nonholonomic systems.This paper presents a design of optimal controllers with respect to a meaningful cost function to globally asymptotically stabilize (in probability) nonholonomic systems affine in stochastic disturbances. The design is based on the Lyapunov direct method, the backstepping technique, and the inverse optimal control design. A class of Lyapunov functions, which are not required to be as nonlinearly strong as quadratic or quartic, is proposed for the control design. Thus, these Lyapunov functions can be applied to design of controllers for underactuated (stochastic) mechanical systems, which are usually required Lyapunov functions of a nonlinearly weak form. The proposed control design is illustrated on a kinematic cart, of which wheel velocities are perturbed by stochastic noise. 2015 Journal Article http://hdl.handle.net/20.500.11937/7294 10.1016/j.sysconle.2014.11.003 http://www.sciencedirect.com/science/article/pii/S0167691114002369 Elsevier BV fulltext |
| spellingShingle | stochastic nonholonomic systems Lyapunov functions Do, Khac Duc Global inverse optimal stabilization of stochastic nonholonomic systems |
| title | Global inverse optimal stabilization of stochastic nonholonomic systems |
| title_full | Global inverse optimal stabilization of stochastic nonholonomic systems |
| title_fullStr | Global inverse optimal stabilization of stochastic nonholonomic systems |
| title_full_unstemmed | Global inverse optimal stabilization of stochastic nonholonomic systems |
| title_short | Global inverse optimal stabilization of stochastic nonholonomic systems |
| title_sort | global inverse optimal stabilization of stochastic nonholonomic systems |
| topic | stochastic nonholonomic systems Lyapunov functions |
| url | http://www.sciencedirect.com/science/article/pii/S0167691114002369 http://hdl.handle.net/20.500.11937/7294 |