The Experts below are selected from a list of 312 Experts worldwide ranked by ideXlab platform
Kazuyuki Aihara - One of the best experts on this subject based on the ideXlab platform.
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Clustered Model Reduction of Large-Scale Bidirectional Networks
Analysis and Control of Complex Dynamical Systems, 2015Co-Authors: Takayuki Ishizaki, Kenji Kashima, Jun-ichi Imura, Kazuyuki AiharaAbstract:This chapter proposes a clustered Model Reduction method for interconnected linear systems evolving over bidirectional networks. This Model Reduction method belongs to a kind of structured Model Reduction methods, where network clustering, namely clustering of subsystems, is performed according to a notion of uncontrollability of local states. We refer to this notion of uncontrollability as cluster reducibility, which can be captured by a coordinate transformation called positive tridiagonal transformation in an algebraic manner. In this chapter, it is shown that the aggregation of the reducible clusters retains the stability of the original system as well as an interconnection topology among clustered subsystems. Furthermore, an \(\fancyscript{H}_{\infty }\)-error bound is derived for the state discrepancy due to the cluster aggregation. The efficiency of the clustered Model Reduction is shown through an example of large-scale complex networks.
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Model Reduction and Clusterization of Large-Scale Bidirectional Networks
IEEE Transactions on Automatic Control, 2014Co-Authors: Takayuki Ishizaki, Kenji Kashima, Jun-ichi Imura, Kazuyuki AiharaAbstract:This paper proposes two Model Reduction methods for large-scale bidirectional networks that fully utilize a network structure transformation implemented as positive tridiagonalization. First, we present a Krylov-based Model Reduction method that guarantees a specified error precision in terms of the H∞-norm. Positive tridiagonalization allows us to derive an approximation error bound for the input-to-state Model Reduction without computationally expensive operations such as matrix factorization. Second, we propose a novel Model Reduction method that preserves network topology among clusters, i.e., node sets. In this approach, we introduce the notion of cluster uncontrollability based on positive tridiagonalization, and then derive its theoretical relation to the approximation error. This error analysis enables us to construct clusters that can be aggregated with a small approximation error. The efficiency of both methods is verified through numerical examples, including a large-scale complex network.
James Lam - One of the best experts on this subject based on the ideXlab platform.
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Internal positivity preserved Model Reduction
International Journal of Control, 2009Co-Authors: Jun-e Feng, James Lam, Zhan Shu, Qing WangAbstract:This article studies Model Reduction of continuous-time stable positive linear systems under the Hankel norm, H∞ norm and H2 norm performance. The reduced-order systems preserve the stability as well as the positivity of the original systems. This is achieved by developing new necessary and sufficient conditions of the Model Reduction performances in which the Lyapunov matrices are decoupled with the system matrices. In this way, the positivity constraints in the reduced-order Model can be imposed in a natural way. As the Model Reduction performances are expressed in linear matrix inequalities with equality constraints, the desired reduced-order positive Models can be obtained by using the cone complementarity linearisation iterative algorithm. A numerical example is presented to illustrate the effectiveness of the given methods. © 2010 Taylor & Francis.link_to_subscribed_fulltex
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h Model Reduction of markovian jump linear systems
Systems & Control Letters, 2003Co-Authors: Liqian Zhang, Biao Huang, James LamAbstract:Abstract In this paper, the H ∞ Model Reduction problem for linear systems that possess randomly jumping parameters is studied. The development includes both the continuous and discrete cases. It is shown that the reduced order Models exist if a set of matrix inequalities is feasible. An effective iterative algorithm involving linear matrix inequalities is suggested to solve the matrix inequalities characterizing the Model Reduction solutions. Using the numerical solutions of the matrix inequalities, the reduced order Models can be obtained. An example is given to illustrate the proposed Model Reduction method.
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H∞ Model Reduction of Markovian jump linear systems☆
Systems & Control Letters, 2003Co-Authors: Liqian Zhang, Biao Huang, James LamAbstract:In this paper, the H∞ Model Reduction problem for linear systems that possess randomly jumping parameters is studied. The development includes both the continuous and discrete cases. It is shown that the reduced order Models exist if a set of matrix inequalities is feasible. An effective iterative algorithm involving linear matrix inequalities is suggested to solve the matrix inequalities characterizing the Model Reduction solutions. Using the numerical solutions of the matrix inequalities, the reduced order Models can be obtained. An example is given to illustrate the proposed Model Reduction method. © 2003 Elsevier B.V. All rights reserved.link_to_subscribed_fulltex
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On H2 Model Reduction of bilinear systems
Automatica, 2002Co-Authors: Liqian Zhang, James LamAbstract:The H"2 Model Reduction problem for continuous-time bilinear systems is studied in this paper. By defining the H"2 norm of bilinear systems in terms of the state-space matrices, the H"2 Model Reduction error is computed via the reachability or observability gramian. Necessary conditions for the reduced order bilinear Models to be H"2 optimal are given. The gradient flow approach is used to obtain the solution of the H"2 Model Reduction problem. The formulation allows certain properties of the original Models to be preserved in the reduced order Models. The Model Reduction procedure developed can also be applied to finite-dimensional linear time-invariant systems. A numerical example is employed to illustrate the effectiveness of the proposed method.
Henrik Sandberg - One of the best experts on this subject based on the ideXlab platform.
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SiMpLIfy: A toolbox for structured Model Reduction
2015 European Control Conference (ECC), 2015Co-Authors: Martin Biel, Farhad Farokhi, Henrik SandbergAbstract:In this paper, we present a toolbox for structured Model Reduction developed for MATLAB. In addition to structured Model Reduction methods using balanced realizations of the subsystems, we introduce a numerical algorithm for structured Model Reduction using a subgradient optimization algorithm. We briefly present the syntax for the toolbox and its features. Finally, we demonstrate the applicability of various Model Reduction methods in the toolbox on a structured mass-spring mechanical system.
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ECC - SiMpLIfy: A toolbox for structured Model Reduction
2015 European Control Conference (ECC), 2015Co-Authors: Martin Biel, Farhad Farokhi, Henrik SandbergAbstract:In this paper, we present a toolbox for structured Model Reduction developed for MATLAB. In addition to structured Model Reduction methods using balanced realizations of the subsystems, we introduce a numerical algorithm for structured Model Reduction using a subgradient optimization algorithm. We briefly present the syntax for the toolbox and its features. Finally, we demonstrate the applicability of various Model Reduction methods in the toolbox on a structured mass-spring mechanical system.
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Model Reduction of interconnected linear systems
Optimal Control Applications & Methods, 2009Co-Authors: Henrik Sandberg, Richard M MurrayAbstract:The problem of Model Reduction of linear systems with certain interconnection structure is considered in this paper. To preserve the interconnection structure between subsystems in the Reduction, special care needs to be taken. This problem is important and timely because of the recent focus on complex networked systems in control engineering. Two different Model Reduction methods are introduced and compared in this paper. Both methods are extensions to the well-known balanced truncation method. Compared with earlier work in the area these methods use a more general linear fractional transformation framework, and utilize linear matrix inequalities. Furthermore, new approximation error bounds that reduce to classical bounds in special cases are derived. The so-called structured Hankel singular values are used in the methods, and indicate how important states in the subsystems are with respect to a chosen input-output map for the entire interconnected system. It is shown how these structured Hankel singular values can be used to select an approximation order. Finally, the two methods are applied to a Model of a mechanical device.
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On Model Reduction of Polynomial Dynamical Systems
Proceedings of the 44th IEEE Conference on Decision and Control, 1Co-Authors: S. Prajna, Henrik SandbergAbstract:In this paper, we develop a computational method for Model Reduction of polynomial dynamical systems. This is achieved using sum of squares relaxations on certain Lyapunov inequalities, which are the nonlinear counterparts of the Lyapunov controllability and observability linear matrix inequalities for linear systems. In our Model Reduction procedure, we use notions of balanced realization and balanced truncation for a polynomial Model. In addition, we derive an a-priori error bound on the approximation error for balanced truncation.
Alessandro Astolfi - One of the best experts on this subject based on the ideXlab platform.
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Nonlinear Model Reduction by Moment Matching
2017Co-Authors: Giordano Scarciotti, Alessandro AstolfiAbstract:Reduced order Models, or Model Reduction, have been used in many technologically advanced areas to ensure the associated complicated mathematical Models remain computable. For instance, reduced order Models are used to simulate weather forecast Models and in the design of very large scale integrated circuits and networked dynamical systems. For linear systems, the Model Reduction problem has been addressed from several perspectives and a comprehensive theory exists. Although many results and efforts have been made, at present there is no complete theory of Model Reduction for nonlinear systems or, at least, not as complete as the theory developed for linear systems. This monograph presents, in a uniform and complete fashion, moment matching techniques for nonlinear systems. This includes extensive sections on nonlinear time-delay systems; moment matching from input/output data and the limitations of the characterization of moment based on a signal generator described by differential equations. Each section is enriched with examples and is concluded with extensive bibliographical notes. This monograph provides a comprehensive and accessible introduction into Model Reduction for researchers and students working on non-linear systems.
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Nonlinear Model Reduction by Moment Matching
Foundations and Trends® in Systems and Control, 2017Co-Authors: Giordano Scarciotti, Alessandro AstolfiAbstract:Mathematical Models are at the core of modern science and technology. An accurate description of behaviors, systems and processes often requires the use of complex Models which are difficult to analyze and control. To facilitate analysis of and design for complex systems, Model Reduction theory and tools allow determining “simpler” Models which preserve some of the features of the underlying complex description. A large variety of techniques, which can be distinguished depending on the features which are preserved in the Reduction process, has been proposed to achieve this goal. One such a method is the moment matching approach. This monograph focuses on the problem of Model Reduction by moment matching for nonlinear systems. The central idea of the method is the preservation, for a prescribed class of inputs and under some technical assumptions, of the steady-state output response of the system to be reduced. We present the moment matching approach from this vantage point, covering the problems of Model Reduction for nonlinear systems, nonlinear time-delay systems, data-driven Model Reduction for nonlinear systems and Model Reduction for “discontinuous” input signals. Throughout the monograph linear systems, with their simple structure and strong properties, are used as a paradigm to facilitate understanding of the theory and provide foundation of the terminology and notation. The text is enriched by several numerical examples, physically motivated examples and with connections to well-established notions and tools, such as the phasor transform
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Model Reduction by moment matching for linear and nonlinear systems
IEEE Transactions on Automatic Control, 2010Co-Authors: Alessandro AstolfiAbstract:The Model Reduction problem for (single-input, single-output) linear and nonlinear systems is addressed using the notion of moment. A re-visitation of the linear theory allows to obtain novel results for linear systems and to develop a nonlinear enhancement of the notion of moment. This, in turn, is used to pose and solve the Model Reduction problem by moment matching for nonlinear systems, to develop a notion of frequency response for nonlinear systems, and to solve Model Reduction problems in the presence of constraints on the reduced Model. Connections between the proposed results, projection methods, the covariance extension problem and interpolation theory are presented. Finally, the theory is illustrated by means of simple worked out examples and case studies.
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Model Reduction BY MOMENT MATCHING
IFAC Proceedings Volumes, 2007Co-Authors: Alessandro AstolfiAbstract:Abstract The Model Reduction problem by moment matching for linear and nonlinear systems is discussed. The linear theory is revisited to provide the basis for the development of the nonlinear theory.
Takayuki Ishizaki - One of the best experts on this subject based on the ideXlab platform.
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Clustered Model Reduction of Large-Scale Bidirectional Networks
Analysis and Control of Complex Dynamical Systems, 2015Co-Authors: Takayuki Ishizaki, Kenji Kashima, Jun-ichi Imura, Kazuyuki AiharaAbstract:This chapter proposes a clustered Model Reduction method for interconnected linear systems evolving over bidirectional networks. This Model Reduction method belongs to a kind of structured Model Reduction methods, where network clustering, namely clustering of subsystems, is performed according to a notion of uncontrollability of local states. We refer to this notion of uncontrollability as cluster reducibility, which can be captured by a coordinate transformation called positive tridiagonal transformation in an algebraic manner. In this chapter, it is shown that the aggregation of the reducible clusters retains the stability of the original system as well as an interconnection topology among clustered subsystems. Furthermore, an \(\fancyscript{H}_{\infty }\)-error bound is derived for the state discrepancy due to the cluster aggregation. The efficiency of the clustered Model Reduction is shown through an example of large-scale complex networks.
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Model Reduction and Clusterization of Large-Scale Bidirectional Networks
IEEE Transactions on Automatic Control, 2014Co-Authors: Takayuki Ishizaki, Kenji Kashima, Jun-ichi Imura, Kazuyuki AiharaAbstract:This paper proposes two Model Reduction methods for large-scale bidirectional networks that fully utilize a network structure transformation implemented as positive tridiagonalization. First, we present a Krylov-based Model Reduction method that guarantees a specified error precision in terms of the H∞-norm. Positive tridiagonalization allows us to derive an approximation error bound for the input-to-state Model Reduction without computationally expensive operations such as matrix factorization. Second, we propose a novel Model Reduction method that preserves network topology among clusters, i.e., node sets. In this approach, we introduce the notion of cluster uncontrollability based on positive tridiagonalization, and then derive its theoretical relation to the approximation error. This error analysis enables us to construct clusters that can be aggregated with a small approximation error. The efficiency of both methods is verified through numerical examples, including a large-scale complex network.
