Adaptive regulation of MIMO linear systems against unknown sinusoidal exogenous inputs
This paper deals with the adaptive regulation problem in linear multi‐input multi‐output systems subject to unknown sinusoidal exogenous inputs, where the frequencies, amplitudes, and phases of the sinusoids are unknown and where the number of sinusoids is assumed to be known. The design of an adapt...
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| Published in | International journal of adaptive control and signal processing Vol. 23; no. 6; pp. 581 - 603 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Chichester, UK
John Wiley & Sons, Ltd
01.06.2009
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0890-6327 1099-1115 |
| DOI | 10.1002/acs.1072 |
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| Abstract | This paper deals with the adaptive regulation problem in linear multi‐input multi‐output systems subject to unknown sinusoidal exogenous inputs, where the frequencies, amplitudes, and phases of the sinusoids are unknown and where the number of sinusoids is assumed to be known. The design of an adaptive regulator for the system under consideration is performed within a set of Q‐parameterized stabilizing controllers. To facilitate the design of the adaptive regulator, triangular decoupling is introduced in part of the closed‐loop system dynamics. This is achieved through the proper selection of the controller state feedback gain and the structure of the Q parameter. Regulation conditions are then presented for the case where the sinusoidal exogenous input properties are known. For the case where the sinusoidal exogenous input properties are unknown, an adaptation algorithm is proposed to tune the Q parameter in the expression of the parameterized controller. The online tuning of the Q parameter allows the controller to converge to the desired regulator. Convergence results of the adaptation algorithm are presented. A simulation example involving a retinal imaging adaptive optics system is used to illustrate the performance of the proposed adaptive system. Copyright © 2008 John Wiley & Sons, Ltd. |
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| AbstractList | This paper deals with the adaptive regulation problem in linear multi-input multi-output systems subject to unknown sinusoidal exogenous inputs, where the frequencies, amplitudes, and phases of the sinusoids are unknown and where the number of sinusoids is assumed to be known. The design of an adaptive regulator for the system under consideration is performed within a set of Q-parameterized stabilizing controllers. To facilitate the design of the adaptive regulator, triangular decoupling is introduced in part of the closed-loop system dynamics. This is achieved through the proper selection of the controller state feedback gain and the structure of the Q parameter. Regulation conditions are then presented for the case where the sinusoidal exogenous input properties are known. For the case where the sinusoidal exogenous input properties are unknown, an adaptation algorithm is proposed to tune the Q parameter in the expression of the parameterized controller. The online tuning of the Q parameter allows the controller to converge to the desired regulator. Convergence results of the adaptation algorithm are presented. A simulation example involving a retinal imaging adaptive optics system is used to illustrate the performance of the proposed adaptive system. This paper deals with the adaptive regulation problem in linear multi‐input multi‐output systems subject to unknown sinusoidal exogenous inputs, where the frequencies, amplitudes, and phases of the sinusoids are unknown and where the number of sinusoids is assumed to be known. The design of an adaptive regulator for the system under consideration is performed within a set of Q ‐parameterized stabilizing controllers. To facilitate the design of the adaptive regulator, triangular decoupling is introduced in part of the closed‐loop system dynamics. This is achieved through the proper selection of the controller state feedback gain and the structure of the Q parameter. Regulation conditions are then presented for the case where the sinusoidal exogenous input properties are known. For the case where the sinusoidal exogenous input properties are unknown, an adaptation algorithm is proposed to tune the Q parameter in the expression of the parameterized controller. The online tuning of the Q parameter allows the controller to converge to the desired regulator. Convergence results of the adaptation algorithm are presented. A simulation example involving a retinal imaging adaptive optics system is used to illustrate the performance of the proposed adaptive system. Copyright © 2008 John Wiley & Sons, Ltd. This paper deals with the adaptive regulation problem in linear multi‐input multi‐output systems subject to unknown sinusoidal exogenous inputs, where the frequencies, amplitudes, and phases of the sinusoids are unknown and where the number of sinusoids is assumed to be known. The design of an adaptive regulator for the system under consideration is performed within a set of Q‐parameterized stabilizing controllers. To facilitate the design of the adaptive regulator, triangular decoupling is introduced in part of the closed‐loop system dynamics. This is achieved through the proper selection of the controller state feedback gain and the structure of the Q parameter. Regulation conditions are then presented for the case where the sinusoidal exogenous input properties are known. For the case where the sinusoidal exogenous input properties are unknown, an adaptation algorithm is proposed to tune the Q parameter in the expression of the parameterized controller. The online tuning of the Q parameter allows the controller to converge to the desired regulator. Convergence results of the adaptation algorithm are presented. A simulation example involving a retinal imaging adaptive optics system is used to illustrate the performance of the proposed adaptive system. Copyright © 2008 John Wiley & Sons, Ltd. |
| Author | Ficocelli, Maurizio Ben Amara, Foued |
| Author_xml | – sequence: 1 givenname: Maurizio surname: Ficocelli fullname: Ficocelli, Maurizio organization: Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ont., Canada M5S 3G8 – sequence: 2 givenname: Foued surname: Ben Amara fullname: Ben Amara, Foued email: benamara@mie.utoronto.ca organization: Department of Mechanical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ont., Canada M5S 3G8 |
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IEEE Transactions on Automatic Control 2007; 52:1232-1248. – reference: Lan W, Chen BM, Ding Z. Adaptive estimation and rejection of unknown sinusoidal disturbances through measurement feedback for a class of non-minimum phase non-linear MIMO systems. International Journal of Adaptive Control and Signal Processing 2006; 20:77-97. – reference: Francis BA, Wonham M. The internal model principle of control theory. Automatica 1976; 12:486-505. – reference: Liang J, Williams DR, Miller DT. Supernormal vision and high-resolution retinal imaging through adaptive optics. Journal of the Optical Society of America A 1997; 14:2884-2892. – reference: Canetti RM, Espana MD. Convergence analysis of the least-squares identification algorithm with a variable forgetting factor for time-varying linear systems. Automatica 1989; 25:609-612. – reference: Ding Z. Adaptive disturbance rejection of nonlinear systems in an extended output feedback form. IET Control Theory and Applications 2007; 1:298-303. – reference: Ding Z. Adaptive estimation and rejection of unknown sinusoidal disturbances in a class of non-minimum-phase nonlinear systems. IEE Proceedings-Control Theory and Applications 2006; 153:379-386. – reference: Ding Z. Asymptotic rejection of unknown sinusoidal disturbances in nonlinear systems. Automatica 2007; 43:174-177. – reference: Koumboulis FN. Input-output triangular decoupling and data sensitivity. Automatica 1996; 32:569-573. – reference: Marino R, Tomei P. Output regulation for linear systems via adaptive internal model. IEEE Transactions on Automatic Control 2003; 48:2199-2202. – reference: Ding Z. Asymptotic rejection of asymmetric periodic disturbances in output-feedback nonlinear systems. Automatica 2007; 43:555-561. – reference: Hofer H, Artal P, Singer B, Aragon JL, Williams DR. Dynamics of the eye's wave aberration. Journal of the Optical Society of America A 2002; 18:497-506. – reference: Isidori A, Byrnes CI. Output regulation of nonlinear systems. IEEE Transactions on Automatic Control 1990; 35:131-140. – reference: Nikiforov VO. Adaptive non-linear tracking with complete compensation of unknown disturbances. European Journal of Control 1998; 4:132-139. – reference: Marino R, Santosuosso GL, Tomei P. Robust adaptive compensation of biased sinusoidal disturbances with unknown frequency. Automatica 2003; 39:1755-1761. – reference: Wu B, Bodson M. Direct adaptive cancellation of periodic disturbances for multivariable plants. IEEE Transactions on Speech and Audio Processing 2003; 11:538-548. – reference: Bodson M, Douglas SC. Adaptive algorithms for the rejection of sinusoidal disturbances with unknown frequency. Automatica 1997; 33:2213-2221. – reference: Bodson B, Jensen JS, Douglas SC. Active noise control for periodic disturbances. 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| Snippet | This paper deals with the adaptive regulation problem in linear multi‐input multi‐output systems subject to unknown sinusoidal exogenous inputs, where the... This paper deals with the adaptive regulation problem in linear multi-input multi-output systems subject to unknown sinusoidal exogenous inputs, where the... |
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| SubjectTerms | Adaptation Adaptive optics adaptive regulation Adaptive systems Algorithms Control Controllers Design engineering multi-input multi-output systems Q parameterization Regulators triangular decoupling |
| Title | Adaptive regulation of MIMO linear systems against unknown sinusoidal exogenous inputs |
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