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On the minimum energy compensation for linear time-varying disturbed systems

Treść / Zawartość
Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider in this work a class of finite dimensional time-varying linear disturbed systems. The main objective of this work is to studied the optimal control which ensures the remediability of a disturbance of time-varying disturbed systems. The remediability concept consist to find a convenient control which bringing back the corresponding observation of disturbed system to the normal one at the final time. We give firstly some characterisations of compensation and in second party we find a control which annul the output of the system and we show also that the Hilbert Uniqueness Method can be used to solve the optimal control which ensure the remediability. A general approach was given to minimize the linear quadratic problem. Examples and numerical simulations are given.
Rocznik
Strony
733--754
Opis fizyczny
Bibliogr. 29 poz., rys., wzory
Twórcy
  • Fundamental and Applied Mathematics Laboratory, Department of Mathematics and Computer Science, Faculty of Sciences Ain Chock, Hassan II University of Casablanca, B.P. 5366-Maârif, Casablanca, Morocco
autor
  • Fundamental and Applied Mathematics Laboratory, Department of Mathematics and Computer Science, Faculty of Sciences Ain Chock, Hassan II University of Casablanca, B.P. 5366-Maârif, Casablanca, Morocco
autor
  • Fundamental and Applied Mathematics Laboratory, Department of Mathematics and Computer Science, Faculty of Sciences Ain Chock, Hassan II University of Casablanca, B.P. 5366-Maârif, Casablanca, Morocco
  • Fundamental and Applied Mathematics Laboratory, Department of Mathematics and Computer Science, Faculty of Sciences Ain Chock, Hassan II University of Casablanca, B.P. 5366-Maârif, Casablanca, Morocco
Bibliografia
  • [1] L. Afifi, M. Bahadi and A. Chafiai: A regional asymptotic analysis of the compensation problem in distributed systems. International Journal of Applied Mathematical Sciences, 1(54), (2007), 2659-2686.
  • [2] L. Afifi, M. Bahadi, A. El Jai and A. El Mizane: The compensation problem in disturbed systems: Asymptotic analysis, Approximations and numerical simulations. International Journal of Pure and Applied Mathematics, 41(7), (2007), 957-967.
  • [3] L. Afifi, A. Chafiai and A. El Jai: Sensors and actuators for compensation in hyperbolic systems. Foorteenth International Symposium of Mathematical Theory of Networks and systems, MTNS’2000, Perpignan, France, (2000).
  • [4] L. Afifi, A. Chafiai and A. El Jai: Spatial Compensation of boundary disturbances by boundary actuators. International Journal of Applied Mathematics and Computer Science, 11(4), (2001), 899-920.
  • [5] L. Afifi, A. Chafiai and A. El Jai: Regionally efficient and strategic actuators. International Journal of Systems Science, 33(1), (2002), 1-12. DOI: 10.1080/002077202317216884.
  • [6] L. Afifi, A. El Jai and E.M. Magri: Compensation problem in flnite dimension linear dynamical systems. International Journal of Applied Mathematical Sciences, 2(45), (2008), 2219-2228.
  • [7] L. Afifi, K. Lasri, M. Joundi and N. Amimi: Feedback controls for exact remediability in disturbed dynamical systems. IMA Journal of Mathematical Control and Information, 35(2), (2018), 411-425. DOI: 10.1093/imamci/dnw054.
  • [8] L. Afifi, K. Lasri, M. Joundi and N. Amimi: Feedback controls for finite time or ssymptotic compensation in lumped disturbed systems. British Journal of Mathematics & Computer Science, 7(3), (2015), 168-180.
  • [9] S. Ben Rhila, M. Lhous and M. Rachik: On the asymptotic output sensitivity problem for a discrete linear systems with uncertain initial state. Mathematical Modeling and Computing, 8(1), (2021), 22-34. DOI: 10.23939/mmc2021.01.022.
  • [10] R.F. Curtain and A.J. Pritchard: Infinite Dimensional Linear Systems Theory. Lecture Notes in Control and Information Sciences, 8, Berlin, 1978.
  • [11] B. Dehman and G. Lebeau: Analysis of the HUM control operator and exact controllability for semilinear waves in uniform time. SIAM Journal of Control and Optimization, 48(2), (2009), 521-550. DOI: 10.1137/070712067.
  • [12] A. El Badia and T. Ha-Duong: Some remarks on the problem of source identification from boundary measurements. Inverse Problems, 14 (1998), 883-891. DOI: 10.1088/0266-5611/14/4/008.
  • [13] M. Isakov: Inverse Problems for Partial Differential Equations. Springer, New York, 1998.
  • [14] T. Kaczorek and K. Borawski: Minimum energy control of descriptor discrete-time linear systems by the use of Weierstrass-Kronecker decomposition. Archives of Control Sciences, 26(2), (2016), 177-187. DOI: 10.1515/acsc-2016-0010.
  • [15] T. Kaczorek: An extension of Klamka’s method to positive descriptor discrete-time linear systems with bounded inputs. Archives of Control Sciences, 28(2), (2018), 255-268. DOI: 10.24425/123459.
  • [16] J.E. Lagnese: The Hilbert uniqueness method: A retrospective. In: K.H. Hoffmann and W. Krabs (eds). Optimal Control of Partial Differential Equations. Lecture Notes in Control and Information Sciences, 149 Springer, Berlin, Heidelberg. DOI: 10.1007/BFb0043222.
  • [17] A. Larrache, M. Lhous, S. Ben Rhila, M. Rachik and A. Tridane: An output sensitivity problem for a class of linear distributed systems with uncertain initial state. Archives of Control Sciences, 30(1), (2020), 77-93. DOI: 10.24425/acs.2020.132589.
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  • [22] A. Nanda and P.C. Das: Determination of the term source in the heat condition equation. Inverse Problems, 12 (1996), 325-339. DOI: 10.1088/0266-5611/12/3/011.
  • [23] Y. Qaraai, A. Bernoussi and A. El Jai: How to compensate a spreading disturbance for a class of nonlinear systems. International Journal of Applied Mathematics and Computer Science, 18(2), (2008), 171-187. DOI: 10.2478/v10006-008-0016-9.
  • [24] sc M. Rachik and M. Lhous: An observer-based control of linear systems with uncertain parameters. Archives of Control Sciences, 26(4), (2016), 565-576. DOI: 10.1515/acsc-2016-0031.
  • [25] S. Rekkab and S. Benhadid: Gradient remediability in linear distributed parabolic systems analysis, approximations and simulations. Journal of Fundamental and Applied Sciences, 9(3), (2017), 1535-1558. DOI: 10.4314/jfas.v9i3.18.
  • [26] M. Skliar and W.F. Ramirez: Source identification in distributed parameter systems. Applied Mathematics and Computer Science, 8(4), (1998), 733754.
  • [27] S. Souhail and L. Afifi: Cheap compensation in disturbed linear dynamical systems with multi-input delays. International Journal of Dynamics and Control, 8 (2020), 243-253. DOI: 10.1007/s40435-018-00505-6.
  • [28] S. Souhail and L. Afifi: Cheap controls for disturbances compensation in hyperbolic delayed systems. International Journal of Dynamical Systems and Differential Equations, 10(6), (2020), 511-536. DOI: 10.1504/IJDSDE.2020.112758.
  • [29] S. Souhail and L. Afifi: Minimum energy compensation for discrete delayed systems with disturbances. Discrete and Continuous Dynamical Systems - S, 13(9), (2020), 2489-2508. DOI: 10.3934/dcdss.2020119.
Uwagi
Opracowanie rekordu ze środków MEiN, umowa nr SONP/SP/546092/2022 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2022-2023)
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-2c268108-eb57-4088-8d7f-cf7a073202e4
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