Model Reference Adaptive Control of 2 \times 2 Coupled Linear Hyperbolic PDEs
We solve a model reference adaptive control problem for a class of linear <inline-formula><tex-math notation="LaTeX"> 2 \times 2</tex-math></inline-formula> hyperbolic partial differential equations (PDEs) with uncertain system parameters subject to harmonic disturb...
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| Published in | IEEE transactions on automatic control Vol. 63; no. 8; pp. 2405 - 2420 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
IEEE
01.08.2018
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| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9286 1558-2523 |
| DOI | 10.1109/TAC.2017.2767378 |
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| Abstract | We solve a model reference adaptive control problem for a class of linear <inline-formula><tex-math notation="LaTeX"> 2 \times 2</tex-math></inline-formula> hyperbolic partial differential equations (PDEs) with uncertain system parameters subject to harmonic disturbances, from a single boundary measurement anticollocated with the actuation. This is done by transforming the system into a canonical form, from which filters are designed so that the states can be expressed as linear combinations of the filters and uncertain parameters, a representation facilitating for the design of adaptive laws. A stabilizing controller is then combined with the adaptive laws to make the measured signal asymptotically track the output of a reference model. The reference model is taken as a simple transport PDE. Moreover, pointwise boundedness of all variables in the closed loop is proved, provided the reference signal is bounded. The theory is demonstrated in a simulation. |
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| AbstractList | We solve a model reference adaptive control problem for a class of linear <inline-formula><tex-math notation="LaTeX"> 2 \times 2</tex-math></inline-formula> hyperbolic partial differential equations (PDEs) with uncertain system parameters subject to harmonic disturbances, from a single boundary measurement anticollocated with the actuation. This is done by transforming the system into a canonical form, from which filters are designed so that the states can be expressed as linear combinations of the filters and uncertain parameters, a representation facilitating for the design of adaptive laws. A stabilizing controller is then combined with the adaptive laws to make the measured signal asymptotically track the output of a reference model. The reference model is taken as a simple transport PDE. Moreover, pointwise boundedness of all variables in the closed loop is proved, provided the reference signal is bounded. The theory is demonstrated in a simulation. |
| Author | Aamo, Ole Morten Anfinsen, Henrik |
| Author_xml | – sequence: 1 givenname: Henrik orcidid: 0000-0002-8234-8830 surname: Anfinsen fullname: Anfinsen, Henrik email: henrik.anfinsen@ntnu.no organization: Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway – sequence: 2 givenname: Ole Morten surname: Aamo fullname: Aamo, Ole Morten email: aamo@ntnu.no organization: Department of Engineering Cybernetics, Norwegian University of Science and Technology, Trondheim, Norway |
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| Cites_doi | 10.1016/j.automatica.2017.06.026 10.1016/j.automatica.2016.02.007 10.1109/TAC.2014.2335374 10.1016/0270-0255(86)90061-8 10.1016/j.sysconle.2015.09.009 10.1016/j.automatica.2016.05.030 10.1016/j.automatica.2007.02.014 10.1109/TAC.2013.2274723 10.1016/j.sysconle.2008.02.005 10.1002/0471459100 10.1109/TAC.2012.2228035 10.1109/CDC.2011.6160338 10.1109/TCST.2012.2204751 10.1007/978-0-8176-4877-0 10.1016/j.automatica.2016.09.020 10.1109/TAC.2006.887903 10.1016/j.ifacol.2016.07.438 10.1002/rnc.3331 10.1109/TAC.2016.2530624 10.1109/TCST.2016.2631511 10.1109/9.975513 10.1515/9781400835362 10.1016/j.automatica.2007.02.015 10.1109/TAC.2015.2398882 10.1016/0022-0396(84)90135-9 10.1109/CDC.2014.7039701 10.1016/j.automatica.2016.10.027 10.1016/j.mcm.2006.01.016 10.1016/j.ifacol.2016.07.447 10.1016/j.sysconle.2017.03.008 10.1109/TAC.2015.2512847 10.1109/TAC.2014.2322435 10.1016/j.automatica.2014.09.001 10.1109/TAC.2008.927798 10.1109/CDC.2006.377703 10.23919/ACC.2017.7963000 10.1016/S0294-1449(02)00004-5 |
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| Title | Model Reference Adaptive Control of 2 \times 2 Coupled Linear Hyperbolic PDEs |
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