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Model reduction problem of linear discrete systems: Admissibles initial states

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Given a linear discrete system with initial state x0 and output function yi , we investigate a low dimensional linear system that produces, with a tolerance index ϵ, the same output function when the initial state belongs to a specified set, called ϵ-admissible set, that we characterize by a finite number of inequalities. We also give an algorithm which allows us to determine an ϵ-admissible set.
Rocznik
Strony
41--55
Opis fizyczny
Bibliogr. 27 poz., wykr., wzory
Twórcy
autor
  • University Ibn Tofail, Faculty of Science, Departmentof Mathematics, B. P. 133, Kénitra Maroc
autor
  • University Hassan II, Faculty of Science Ben M’Sik, Department of Mathematics, Casablanca Maroc
Bibliografia
  • [1] A. C. Antoulas and D. C. Sorensen: Projection methods for balanced model reduction, Technical Report ECE-CAAM Depts, Rice University, 1999.
  • [2] A. C. Antoulas and D. C. Sorensen: The Sylvester equation and approximate balanced reduction, Fourth Special Issue on Linear Systems and Control, V. Blondel, D. Hinrichsen, J. Rosenthal, and P. M. van Dooren, Linear Algebra and Its Applications (2002), 351–352: 671–700.
  • [3] U. Baur, P. Benner, and L. Feng: Model order reduction for linear and nonlinear systems: a system-theoretic perspective, Archives of Computational Methods in Engineering, 21(4) (2014), doi: 10.1007/s11831-014-9111-2.
  • [4] D. Bonvin and D. A. Mellichamp: A Generalised Structural Dominance Method for the Analysis of Large Scale Systems, International Journal of Control, 35(5) (1982), 807–827.
  • [5] D. Chaniotis and M. A. Pai: Model Reduction in Power Systems using Krylov Subspace Methods, IEEE Transactions on Power Systems, 20(2) (2002), 888–894.
  • [6] E. J. Davison: A Method for Simplifying Linear Dynamic Systems, IEEE Transactions on Automatic Control, 11(1) (1966), 93–101.
  • [7] V. F. Demyanov and A. M. Rubinov: Foundations of non-smooth analysis and quasidifferential calculus, Nauka, Moscow (1990), 124–125 [in Russian].
  • [8] S. D. Dukié and A. T. Sarié: Dynamic model reduction: An overview of available techniques with application to power systems, Serbian Journal of Electrical Engineering, 9(2) (2012), 131–169.
  • [9] E. G. Gilbert and K. Tin Tan: Linear systems with state and control constraints: The theory and application of maximal output admissible sets, Ieee Transaction on Automatic Control, 36(9) (1991), 1008–1019.
  • [10] S. Gugercin and A. C. Antoulas: A survey ofmodel reduction by balanced truncation and some new results, International Journal of Control, 77(8) (2004), 748–766.
  • [11] S. Gugercin and A. C. Antoulas: Model reduction of large scale systems by least squares, Linear Algebra and its Applications, 415(2-3) (2006), 290–321.
  • [12] H. Hadwiger: Vorlesungen uber Inhalt, Oberflaache und Isoperimetrie, Springer, Berlin, 1957.
  • [13] J. Hahn and T. F. Edgar: An Improved Method for Nonlinear Model Reduction using Balancing of Empirical Gramians, Computers and Chemical Engineering, 26(10) (2002), 1379–1397.
  • [14] J. Hahn and T. F. Edgar: A balancing approach to minimal realization and model reduction of stable nonlinear systems, Industrial and Engineering Chemical Research, 41(9) (2002), 2204–2212.
  • [15] M. A. Johnson and M. W. Daniels: Identification of essential states for reduced-order models using a modal analysis, IEEE Proceedings D on Control Theory and Applications, 132(3) (1985), 111–118.
  • [16] P. V. Kokotovic, R. E. O’Malley, and P. Sannuti: Singular perturbation and order reduction in control theory – An Overview, Automatica, 12(2) (1976), 123–132.
  • [17] I. Kolmanovsky and E. G.Gilbert: Theory and computation of disturbance invariant sets for discrete-time linear systems, Mathematical Problems in Engineering: Theory, Methods and Applications, 4 (1998), 317–367.
  • [18] L. Litz: Order reduction of linear state space models via optimal approximation of the non-dominant modes, IFAC Symposium, Toulouse, France, 24-26 June (1980), 195–202.
  • [19] B. C. Moore: Principal component analysis in linear systems: Controllability, observability and model reduction, IEEE Transactions on Automatic Control, 26(1) (1981), 17–32.
  • [20] L. T. Pillage and R. A. Rohrer: Efficient linear circuit analysis by padé approximation via the Lanczos Process, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 14(5) (1990), 639–649.
  • [21] L. S. Pontryagin: Linear differential games, SovietMath.Dokl., 8(3) (1967), 769–771.
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  • [23] M. Rachik and A. Abdelhak: On the admissible perturbations for discrete systems, Journal Archives of Control Sciences, XLVIII(3) (2002), 301–313.
  • [24] M. Rachik, A. Abdelhak, and E. Labriji: On the tolerable initial states: Discrete systems, Applied Mathematical Sciences, 3(9) (2009), 429–442.
  • [25] V. R. Saksena, J. O’Reilly, and P. V. Kokotovic: Singular perturbation and time-scale methods in control theory-survey, Automatica, 20(3) (1984), 273–293.
  • [26] R. Schneider: Convex Bodies: the Brunn-Minkowski theory, Cambridge University Press, 1993.
  • [27] K. Willcox and J. Peraire: Balanced model reduction via the proper orthogonal decomposition, AIAA Journal, 40(11) (2002), 2323–2330.
Uwagi
PL
Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-78b27036-14cc-40ba-bdb1-360bbc2123ab
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