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Extremal problems for second order hyperbolic systems involving multiple time delays

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Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Extremal problems for multiple time delay hyperbolic systems are presented. The optimal boundary control problems for hyperbolic systems in which multiple time delays appear both in the state equations and in the Neumann boundary conditions are solved. The time horizon is fixed. Making use of Dubovicki-Milutin scheme, necessary and sufficient conditions of optimality for the Neumann problem with the quadratic performance functionals and constrained control are derived.
Rocznik
Strony
101--126
Opis fizyczny
Bibliogr. 21 poz., wzory
Twórcy
  • AGH University of Science and Technology, Institute of Automatic Control and Robotics, 30-059 Cracow, al. Mickiewicza 30, Poland
Bibliografia
  • [1] P.D. Christofides and P. Daoutidis: Feedback control of hyperbolic PDE systems. AIChE Journal, 42(11), (1996), 3063-3086. DOI: 10.1002/aic.690421108.
  • [2] P.D. Christofides and P. Daoutidis: Robust control of hyperbolic PDE systems. Chemical Engineering Science, 53(1), (1998), 85-105. DOI: 10.1016/S0009-2509(97)87571-9.
  • [3] P.D. Christofides and P. Daoutidis: Distributed output feedback control of two-time-scale hyperbolic PDE systems. International Journal of Applied Mathematics and Computer Science, 8(4), (1998), 713-732.
  • [4] E.S. Gilbert: An iterative procedure for computing the minimum of a quadratic form on a convex set. SIAM Journal of Control, 4(1), (1966), 61-80. DOI: 10.1137/0304007.
  • [5] I.V. Girsanov: Lectures on the Mathematical Theory of Extremal Problems. Publishing House of the University of Moscow, Moscow, 1970, (in Russian).
  • [6] A. Kowalewski: On optimal control problem for parabolic-hyperbolic system. Problems of Control and Information Theory, 15(5), (1986), 349-359.
  • [7] A. Kowalewski and J. Duda: On some optimal control problem for a parabolic system with boundary condition involving a time-varying lag. IMA Journal of Mathematical Control and Information, 9(2), (1992), 131-146. DOI: 10.1093/imamci/9.2.131.
  • [8] A. Kowalewski: Boundary control problem of a hyperbolic systems with time lags. IMA Journal of Mathematical Control and Information, 10(3), (1993), 261-272. DOI: 10.1093/imamci/10.3.261.
  • [9] A. Kowalewski: Optimal control of distributed parabolic systems with multiple time-varying lags. International Journal of Control, 69(3), (1998), 361-381. DOI: 10.1080/002071798222712.
  • [10] A. Kowalewski: Optimal control of a distributed hyperbolic system with multiple time-varying lags. International Journal of Control, 71(3), (1998), 419-435. DOI: 10.1080/002071798221759.
  • [11] A. Kowalewski and M. Miśkowicz: Extremal problems for time lag parabolic systems. Proceedings of the 21st International Conference of Process Control (PC), Strbske Pleso, Slovakia, (2017), 446-451. DOI: 10.1109/PC.2017.7976255.
  • [12] A. Kowalewski: Extremal problems for distributed parabolic systems with boundary conditions involving time-varying lags. Proceedings of the 22nd International Conference on Methods and Models in Automation and Robotics (MMAR), Międzyzdroje, Poland, (2017), 447-452. DOI: 10.1109/MMAR.2017.8046869.
  • [13] A. Kowalewski: Extremal problems for parabolic systems with time-varying lags. Archives of Control Sciences, 28(1), (2018), 89-104. DOI: 10.24425/119078.
  • [14] A. Kowalewski: Extremal problems for infinite order parabolic systems with time-varying lags. Advances Intelligent Systems and Computing, 1196 (2020), Springer Nature Switzerland AG. DOI: 10.1007/978-3-030-50936-1_1.
  • [15] A. Kowalewski: Extremal problems for parabolic systems with multiple time-varying lags. Proceedings of 23rd International Conference on Methods and Models in Automation and Robotics (MMAR), Międzyzdroje, Poland, (2018), 791-796. DOI: 10.1109/MMAR.2018.8485815.
  • [16] A. Kowalewski and M. Miśkowicz: Extremal problems for integral time lag parabolic systems. Proceedings of the 24th International Conference on Methods and Models in Automation and Robotics (MMAR), Międzyzdroje, Poland, (2019), 7-12. DOI: 10.1109/MMAR.2019.8864638.
  • [17] A. Kowalewski: Extremal problems for time lag hyperbolic systems. Proceedings of the 25th International Conference on Methods and Models in Automation and Robotics (MMAR), Międzyzdroje, Poland, (2021), 245-250. DOI: 10.1109/MMAR49549.2021.9528456.
  • [18] A. Kowalewski: Optimal Control of Infinite Dimensional Distributed Parameter Systems with Delays. AGH University of Science and Technology Press, Cracow, 2001.
  • [19] J.L. Lions: Optimal Control of Systems Governed by Partial Differential Equations. Springer-Verlag, Berlin, 1971.
  • [20] J.L. Lions and E. Magenes: Non-Homogeneous Boundary Value Problems and Applications. vols. 1 and 2, Springer-Verlag, Berlin, 1972.
  • [21] V.P. Maslov: Operators Methods. Publisher “Science”, Moscow, 1973, (in Russian).
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-dd365010-2766-4f22-b34b-3303388ef472
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