The Experts below are selected from a list of 126 Experts worldwide ranked by ideXlab platform
Jacquelien M.a. Scherpen - One of the best experts on this subject based on the ideXlab platform.
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Singular Value Analysis Of Nonlinear Symmetric Systems
IEEE Transactions on Automatic Control, 2011Co-Authors: Tudor C. Ionescu, Kenji Fujimoto, Jacquelien M.a. ScherpenAbstract:In this paper, we introduce the notions of state-space symmetry for nonlinear systems and of the cross operator as a nontrivial natural extension of the linear symmetric case, in terms of the controllability and observability operators associated to it. We give a characterization of a symmetric nonlinear system in terms of the cross operator and a coordinate transformation. Then we analyze the use of the cross operator for solving the Hankel Singular Value problem of the system. The result is a new and simpler characterization of the solutions of this problem in terms of the cross operator and a metric.
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Dissipativity preserving balancing for nonlinear systems - A Hankel operator approach
Systems & Control Letters, 2010Co-Authors: Tudor C. Ionescu, Kenji Fujimoto, Jacquelien M.a. ScherpenAbstract:Abstract In this paper we present a version of balancing for nonlinear systems which is dissipative with respect to a general quadratic supply rate that depends on the input and the output of the system. We discuss an approach that allows us to apply the theory of balancing based upon Hankel Singular Value analysis. In order to do that we prove that the available storage and the required supply of the original system are the controllability and the observability functions of a modified, asymptotically stable, system. Then Hankel Singular Value theory can be applied and the axis Singular Value functions of the modified system equal the nonlinear extensions of “similarity invariants” obtained from the required supply and available storage of the original system. Furthermore, we also consider an extension of normalized comprime factorizations and relate the available storage and required supply with the controllability and observability functions of the factorizations. The obtained relations are used to perform model order reduction based on balanced truncation, yielding dissipative reduced order models for the original systems. A second order electrical circuit example is included to illustrate the results.
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Dissipativity preserving balancing for nonlinear systems — A Hankel operator approach
Systems & Control Letters, 2010Co-Authors: Tudor C. Ionescu, Kenji Fujimoto, Jacquelien M.a. ScherpenAbstract:In this paper we present a version of balancing for nonlinear systems which is dissipative with respect to a general quadratic supply rate that depends on the input and the output of the system. We discuss an approach that allows us to apply the theory of balancing based upon Hankel Singular Value analysis. In order to do that we prove that the available storage and the required supply of the original system are the controllability and the observability functions of a modified, asymptotically stable, system. Then Hankel Singular Value theory can be applied and the axis Singular Value functions of the modified system equal the nonlinear extensions of "similarity invariants" obtained from the required supply and available storage of the original system. Furthermore, we also consider an extension of normalized comprime factorizations and relate the available storage and required supply with the controllability and observability functions of the factorizations. The obtained relations are used to perform model order reduction based on balanced truncation, yielding dissipative reduced order models for the original systems. A second order electrical circuit example is included to illustrate the results. (C) 2010 Elsevier B.V. All rights reserved
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ECC - The cross operator and the Singular Value analysis for nonlinear symmetric systems
2009 European Control Conference (ECC), 2009Co-Authors: Tudor C. Ionescu, Kenji Fujimoto, Jacquelien M.a. ScherpenAbstract:In this paper, we introduce the notions of state-space symmetry for nonlinear systems and of the cross operator as a nontrivial natural extension of the linear symmetric case, in terms of the controllability and observability operators associated to it. We give a characterization of a symmetric nonlinear system in terms of the cross operator and a coordinate transformation. Then we analyze the use of the cross operator for solving the Hankel Singular Value problem of the system. The result is a new and simpler characterization of the solutions of this problem in terms of the cross operator and a metric.
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Hankel Singular Value functions from schmidt pairs for nonlinear input output systems
Systems & Control Letters, 2005Co-Authors: Steven W Gray, Jacquelien M.a. ScherpenAbstract:This paper presents three results in Singular Value analysis of Hankel operators for nonlinear input–output systems. First, the notion of a Schmidt pair is defined for a nonlinear Hankel operator. This makes it possible to define a Hankel Singular Value function from a purely input–output point of view and without introducing a state space setting. However, if a state space realization is known to exist then a set of sufficient conditions is given for the existence of a Schmidt pair, and the state space provides a convenient representation of the corresponding Singular Value function. Finally, it is shown that in a specific coordinate frame it is possible to relate this new Singular Value function definition to the original state space notion used to describe nonlinear balanced realizations.
W.s. Gray - One of the best experts on this subject based on the ideXlab platform.
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Hankel Singular Value functions from Schmidt pairs for nonlinear input–output systems
Systems & Control Letters, 2005Co-Authors: W.s. Gray, Jacquelien M.a. ScherpenAbstract:This paper presents three results in Singular Value analysis of Hankel operators for nonlinear input–output systems. First, the notion of a Schmidt pair is defined for a nonlinear Hankel operator. This makes it possible to define a Hankel Singular Value function from a purely input–output point of view and without introducing a state space setting. However, if a state space realization is known to exist then a set of sufficient conditions is given for the existence of a Schmidt pair, and the state space provides a convenient representation of the corresponding Singular Value function. Finally, it is shown that in a specific coordinate frame it is possible to relate this new Singular Value function definition to the original state space notion used to describe nonlinear balanced realizations.
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Hankel Singular Value functions from Schmidt pairs for nonlinear input-output systems
Proceedings of the 2002 American Control Conference (IEEE Cat. No.CH37301), 2002Co-Authors: W.s. Gray, Jacquelien M.a. ScherpenAbstract:In this paper three results are presented in Singular Value analysis of Hankel operators for nonlinear input-output systems. First the notion of a Schmidt pair is introduced which makes it possible to describe a Hankel Singular Value function from a purely input-output point of view. If a state space realization is known to exist then a set of sufficient conditions is provided for the existence of a Schmidt pair. Finally, it is shown that in a certain coordinate frame it is possible to relate this new Singular Value function definition to the existing definition due to Scherpen (1993, 1995).
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Nonlinear Hilbert adjoints: properties and applications to Hankel Singular Value analysis
Proceedings of the 2001 American Control Conference. (Cat. No.01CH37148), 2001Co-Authors: W.s. Gray, Jacquelien M.a. ScherpenAbstract:The notion of an adjoint operator for a nonlinear mapping has few interpretations in the literature. In this paper a nonlinear Hilbert adjoint operator is proposed. It is shown to unite several existing concepts and provides an essential tool for Singular Value analysis of nonlinear Hankel operators.
Tudor C. Ionescu - One of the best experts on this subject based on the ideXlab platform.
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Singular Value Analysis Of Nonlinear Symmetric Systems
IEEE Transactions on Automatic Control, 2011Co-Authors: Tudor C. Ionescu, Kenji Fujimoto, Jacquelien M.a. ScherpenAbstract:In this paper, we introduce the notions of state-space symmetry for nonlinear systems and of the cross operator as a nontrivial natural extension of the linear symmetric case, in terms of the controllability and observability operators associated to it. We give a characterization of a symmetric nonlinear system in terms of the cross operator and a coordinate transformation. Then we analyze the use of the cross operator for solving the Hankel Singular Value problem of the system. The result is a new and simpler characterization of the solutions of this problem in terms of the cross operator and a metric.
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Dissipativity preserving balancing for nonlinear systems - A Hankel operator approach
Systems & Control Letters, 2010Co-Authors: Tudor C. Ionescu, Kenji Fujimoto, Jacquelien M.a. ScherpenAbstract:Abstract In this paper we present a version of balancing for nonlinear systems which is dissipative with respect to a general quadratic supply rate that depends on the input and the output of the system. We discuss an approach that allows us to apply the theory of balancing based upon Hankel Singular Value analysis. In order to do that we prove that the available storage and the required supply of the original system are the controllability and the observability functions of a modified, asymptotically stable, system. Then Hankel Singular Value theory can be applied and the axis Singular Value functions of the modified system equal the nonlinear extensions of “similarity invariants” obtained from the required supply and available storage of the original system. Furthermore, we also consider an extension of normalized comprime factorizations and relate the available storage and required supply with the controllability and observability functions of the factorizations. The obtained relations are used to perform model order reduction based on balanced truncation, yielding dissipative reduced order models for the original systems. A second order electrical circuit example is included to illustrate the results.
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Dissipativity preserving balancing for nonlinear systems — A Hankel operator approach
Systems & Control Letters, 2010Co-Authors: Tudor C. Ionescu, Kenji Fujimoto, Jacquelien M.a. ScherpenAbstract:In this paper we present a version of balancing for nonlinear systems which is dissipative with respect to a general quadratic supply rate that depends on the input and the output of the system. We discuss an approach that allows us to apply the theory of balancing based upon Hankel Singular Value analysis. In order to do that we prove that the available storage and the required supply of the original system are the controllability and the observability functions of a modified, asymptotically stable, system. Then Hankel Singular Value theory can be applied and the axis Singular Value functions of the modified system equal the nonlinear extensions of "similarity invariants" obtained from the required supply and available storage of the original system. Furthermore, we also consider an extension of normalized comprime factorizations and relate the available storage and required supply with the controllability and observability functions of the factorizations. The obtained relations are used to perform model order reduction based on balanced truncation, yielding dissipative reduced order models for the original systems. A second order electrical circuit example is included to illustrate the results. (C) 2010 Elsevier B.V. All rights reserved
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ECC - The cross operator and the Singular Value analysis for nonlinear symmetric systems
2009 European Control Conference (ECC), 2009Co-Authors: Tudor C. Ionescu, Kenji Fujimoto, Jacquelien M.a. ScherpenAbstract:In this paper, we introduce the notions of state-space symmetry for nonlinear systems and of the cross operator as a nontrivial natural extension of the linear symmetric case, in terms of the controllability and observability operators associated to it. We give a characterization of a symmetric nonlinear system in terms of the cross operator and a coordinate transformation. Then we analyze the use of the cross operator for solving the Hankel Singular Value problem of the system. The result is a new and simpler characterization of the solutions of this problem in terms of the cross operator and a metric.
Kenji Fujimoto - One of the best experts on this subject based on the ideXlab platform.
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Singular Value Analysis Of Nonlinear Symmetric Systems
IEEE Transactions on Automatic Control, 2011Co-Authors: Tudor C. Ionescu, Kenji Fujimoto, Jacquelien M.a. ScherpenAbstract:In this paper, we introduce the notions of state-space symmetry for nonlinear systems and of the cross operator as a nontrivial natural extension of the linear symmetric case, in terms of the controllability and observability operators associated to it. We give a characterization of a symmetric nonlinear system in terms of the cross operator and a coordinate transformation. Then we analyze the use of the cross operator for solving the Hankel Singular Value problem of the system. The result is a new and simpler characterization of the solutions of this problem in terms of the cross operator and a metric.
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Dissipativity preserving balancing for nonlinear systems - A Hankel operator approach
Systems & Control Letters, 2010Co-Authors: Tudor C. Ionescu, Kenji Fujimoto, Jacquelien M.a. ScherpenAbstract:Abstract In this paper we present a version of balancing for nonlinear systems which is dissipative with respect to a general quadratic supply rate that depends on the input and the output of the system. We discuss an approach that allows us to apply the theory of balancing based upon Hankel Singular Value analysis. In order to do that we prove that the available storage and the required supply of the original system are the controllability and the observability functions of a modified, asymptotically stable, system. Then Hankel Singular Value theory can be applied and the axis Singular Value functions of the modified system equal the nonlinear extensions of “similarity invariants” obtained from the required supply and available storage of the original system. Furthermore, we also consider an extension of normalized comprime factorizations and relate the available storage and required supply with the controllability and observability functions of the factorizations. The obtained relations are used to perform model order reduction based on balanced truncation, yielding dissipative reduced order models for the original systems. A second order electrical circuit example is included to illustrate the results.
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Dissipativity preserving balancing for nonlinear systems — A Hankel operator approach
Systems & Control Letters, 2010Co-Authors: Tudor C. Ionescu, Kenji Fujimoto, Jacquelien M.a. ScherpenAbstract:In this paper we present a version of balancing for nonlinear systems which is dissipative with respect to a general quadratic supply rate that depends on the input and the output of the system. We discuss an approach that allows us to apply the theory of balancing based upon Hankel Singular Value analysis. In order to do that we prove that the available storage and the required supply of the original system are the controllability and the observability functions of a modified, asymptotically stable, system. Then Hankel Singular Value theory can be applied and the axis Singular Value functions of the modified system equal the nonlinear extensions of "similarity invariants" obtained from the required supply and available storage of the original system. Furthermore, we also consider an extension of normalized comprime factorizations and relate the available storage and required supply with the controllability and observability functions of the factorizations. The obtained relations are used to perform model order reduction based on balanced truncation, yielding dissipative reduced order models for the original systems. A second order electrical circuit example is included to illustrate the results. (C) 2010 Elsevier B.V. All rights reserved
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ECC - The cross operator and the Singular Value analysis for nonlinear symmetric systems
2009 European Control Conference (ECC), 2009Co-Authors: Tudor C. Ionescu, Kenji Fujimoto, Jacquelien M.a. ScherpenAbstract:In this paper, we introduce the notions of state-space symmetry for nonlinear systems and of the cross operator as a nontrivial natural extension of the linear symmetric case, in terms of the controllability and observability operators associated to it. We give a characterization of a symmetric nonlinear system in terms of the cross operator and a coordinate transformation. Then we analyze the use of the cross operator for solving the Hankel Singular Value problem of the system. The result is a new and simpler characterization of the solutions of this problem in terms of the cross operator and a metric.
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Balancing and model reduction for discrete-time nonlinear systems based on Hankel Singular Value analysis
2004Co-Authors: Kenji Fujimoto, Jacquelien M.a. ScherpenAbstract:This paper is concerned with balanced realization and model reduction for discrete-time nonlinear systems. Singular perturbation type balanced truncation method is proposed. In this procedure, the Hankel Singular Values and the related controllability and observability properties are preserved, which is a natural generalization of both the linear discrete-time case and the nonlinear continuous-time case.
Tomomichi Hagiwara - One of the best experts on this subject based on the ideXlab platform.
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Published online in Wiley InterScience (www.interscience.wiley.com) DOI: 10.1002/asjc.035 ONH ∞ MODELREDUCTION FORDISCRETE-TIME LINEAR TIME-INVARIANT SYSTEMSUSING LINEARMATRIX INEQUALITIES
2015Co-Authors: Yoshio Ebihara, Yoshito Hirai, Tomomichi HagiwaraAbstract:In this paper, we address the H ∞ model reduction problem for linear time-invariant discrete-time systems. We revisit this problem by means of linear matrix inequality (LMI) approaches and first show a concise proof for the well-known lower bounds on the approximation error, which is given in terms of the Hankel Singular Values of the system to be reduced. In addition, when we reduce the system order by the multiplicity of the smallest Hankel Singular Value, we show that the H ∞ optimal reduced-order model can readily be constructed via LMI optimization. These results can be regarded as complete counterparts of those recently obtained in the continuous-time system setting. Key Words: H ∞ model reduction, discrete-time LTI systems, LMI. I
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On H∞ model reduction for discrete-time linear time-invariant systems using linear matrix inequalities
Asian Journal of Control, 2008Co-Authors: Yoshio Ebihara, Yoshito Hirai, Tomomichi HagiwaraAbstract:In this paper, we address the ℋ∞ model reduction problem for linear time-invariant discrete-time systems. We revisit this problem by means of linear matrix inequality (LMI) approaches and first show a concise proof for the well-known lower bounds on the approximation error, which is given in terms of the Hankel Singular Values of the system to be reduced. In addition, when we reduce the system order by the multiplicity of the smallest Hankel Singular Value, we show that the ℋ∞ optimal reduced-order model can readily be constructed via LMI optimization. These results can be regarded as complete counterparts of those recently obtained in the continuous-time system setting.
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On model reduction using LMI's
Proceedings of the 2004 American Control Conference, 2004Co-Authors: Yoshio Ebihara, Tomomichi HagiwaraAbstract:We deal with the problem of approximating a given n-th order LTI system G by an r-th order system Gr where r < n. It is shown that lower bounds of the H/sub /spl infin// norm of the associated error system can be analyzed by using LMI-related techniques. These lower bounds are given in terms of the Hankel Singular Values of the system G and coincide with those obtained in the previous studies where the analysis of the Hankel operators plays a central role. Thus, this paper provides an alternative proof for those lower bounds via simple algebraic manipulations related to LMI's. Moreover, when we reduce the system order by the multiplicity of the smallest Hankel Singular Value, we show that the problem is essentially convex and the optimal reduced-order models can be constructed via LMI optimization.
