On the State-Space Realization of LPV Input-Output Models: Practical Approaches
A common problem in the context of linear parameter-varying (LPV) systems is how input-output (IO) models can be efficiently realized in terms of state-space (SS) representations. The problem originates from the fact that in the LPV literature discrete-time identification and modeling of LPV systems...
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| Veröffentlicht in: | IEEE transactions on control systems technology Jg. 20; H. 1; S. 139 - 153 |
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| Sprache: | Englisch |
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IEEE
01.01.2012
Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
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| Abstract | A common problem in the context of linear parameter-varying (LPV) systems is how input-output (IO) models can be efficiently realized in terms of state-space (SS) representations. The problem originates from the fact that in the LPV literature discrete-time identification and modeling of LPV systems is often accomplished via IO model structures. However, to utilize these LPV-IO models for control synthesis, commonly it is required to transform them into an equivalent SS form. In general, such a transformation is complicated due to the phenomenon of dynamic dependence (dependence of the resulting representation on time-shifted versions of the scheduling signal). This conversion problem is revisited and practically applicable approaches are suggested which result in discrete-time SS representations that have only static dependence (dependence on the instantaneous value of the scheduling signal). To circumvent complexity, a criterion is also established to decide when an linear-time invariant (LTI)-type of realization approach can be used without introducing significant approximation error. To reduce the order of the resulting SS realization, an LPV Ho-Kalman-type of model reduction approach is introduced, which, besides its simplicity, is capable of reducing even non-stable plants. The proposed approaches are illustrated by application oriented examples. |
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| AbstractList | A common problem in the context of linear parameter-varying (LPV) systems is how input-output (IO) models can be efficiently realized in terms of state-space (SS) representations. The problem originates from the fact that in the LPV literature discrete-time identification and modeling of LPV systems is often accomplished via IO model structures. However, to utilize these LPV-IO models for control synthesis, commonly it is required to transform them into an equivalent SS form. In general, such a transformation is complicated due to the phenomenon of dynamic dependence (dependence of the resulting representation on time-shifted versions of the scheduling signal). This conversion problem is revisited and practically applicable approaches are suggested which result in discrete-time SS representations that have only static dependence (dependence on the instantaneous value of the scheduling signal). To circumvent complexity, a criterion is also established to decide when an linear-time invariant (LTI)-type of realization approach can be used without introducing significant approximation error. To reduce the order of the resulting SS realization, an LPV Ho-Kalman-type of model reduction approach is introduced, which, besides its simplicity, is capable of reducing even non-stable plants. The proposed approaches are illustrated by application oriented examples. |
| Author | Werner, H. Toth, R. Abbas, H. S. |
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| Keywords | System realization Kalman filter Dynamic dependence model reduction Linear parameter varying system State space Scheduling State space method Linear control state-space (SS) representation realization Time varying system Linear time invariant system Instantaneous value input-output (IO) representation Discrete time Approximation error Delay time Reduced order systems System identification linear parameter-varying (LPV) systems State estimation Input output model |
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| References_xml | – ident: ref8 doi: 10.1002/rnc.706 – volume: 13 start-page: 733 year: 1994 ident: ref33 article-title: Krylov space methods on state-space control models publication-title: Circuits Syst Signal Process doi: 10.1007/BF02523124 – ident: ref9 doi: 10.3182/20080706-5-KR-1001.00676 – year: 2006 ident: ref25 publication-title: User manual of the linear fractional representation toolbox Version 2 0 – ident: ref29 doi: 10.1016/S0377-0427(00)00341-1 – ident: ref5 doi: 10.1016/j.automatica.2005.08.020 – ident: ref15 doi: 10.1109/CDC.2006.377768 – start-page: 2646 year: 2009 ident: ref10 article-title: An instrumental variable technique for open-loop and closed-loop identification of input-output LPV models publication-title: Proc Euro Control Conf – ident: ref14 doi: 10.1109/MED.2012.6265675 – ident: ref34 doi: 10.1016/j.conengprac.2009.06.005 – start-page: 5418 year: 2007 ident: ref16 article-title: Discrete time LPV I/O and state space representations, differences of behavior and pitfalls of interpolation publication-title: Proc Euro Control Conf – year: 0 ident: ref17 article-title: The behavioral approach to linear parameter-varying systems publication-title: IEEE Trans Autom Control – ident: ref18 doi: 10.1109/MCS.2007.906923 – ident: ref2 doi: 10.1016/j.envsoft.2004.09.015 – ident: ref22 doi: 10.1016/j.sysconle.2005.07.006 – ident: ref21 doi: 10.1109/ACC.1997.609484 – ident: ref6 doi: 10.23919/ECC.2009.7074932 – ident: ref11 doi: 10.1016/j.automatica.2010.02.026 – ident: ref4 doi: 10.1002/(SICI)1099-1239(199611)6:9/10<929::AID-RNC260>3.0.CO;2-9 – year: 2006 ident: ref20 publication-title: System Identification Toolbox for use with MATLAB – ident: ref26 doi: 10.1109/CDC.2000.914153 – ident: ref31 doi: 10.1016/j.automatica.2008.08.015 – ident: ref36 doi: 10.1016/0005-1098(95)00038-X – year: 2000 ident: ref35 publication-title: Neural Networks for Modeling and Control of Dynamic Systems doi: 10.1007/978-1-4471-0453-7 – ident: ref13 doi: 10.1016/j.conengprac.2005.01.013 – ident: ref1 doi: 10.2514/1.9165 – ident: ref32 doi: 10.1137/0305005 – volume: 11 start-page: 303 year: 1993 ident: ref27 article-title: Coprime factors model reduction based on accuracy enhancing techniques publication-title: Syst Anal Model Simulation – ident: ref23 doi: 10.1109/CDC.1996.574345 – ident: ref12 doi: 10.1016/j.conengprac.2004.03.008 – volume: 40 start-page: 853 year: 1995 ident: ref3 article-title: A convex characterization of gain-scheduled <formula formulatype="inline"><tex Notation="TeX">$ {\cal H}_{\infty}$</tex> </formula> controllers publication-title: IEEE Trans Autom Control doi: 10.1109/9.384219 – volume: 403 year: 2010 ident: ref7 publication-title: Ser Lecture Notes in Control and Information Sciences doi: 10.1007/978-3-642-13812-6 – year: 1999 ident: ref19 publication-title: System Identification Theory for the User – ident: ref28 doi: 10.1080/13873959508837010 – ident: ref24 doi: 10.1016/j.ast.2004.12.001 – ident: ref30 doi: 10.1016/j.automatica.2007.02.027 |
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| SubjectTerms | Applied sciences Approximation Approximation error Atmospheric modeling Computer science; control theory; systems Control system analysis Control theory. Systems Dynamic dependence Dynamic scheduling Dynamical systems Dynamics Equivalence Exact sciences and technology input-output (IO) representation linear parameter-varying (LPV) systems Markov processes Mathematical analysis model reduction Modelling and identification Operational research and scientific management Operational research. Management science Polynomials realization Representations Scheduling Scheduling, sequencing state-space (SS) representation Studies Trajectory Transformations |
| Title | On the State-Space Realization of LPV Input-Output Models: Practical Approaches |
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