Feedback design of differential equations of reconstruction for second-order distributed parameter systems

• Autorzy: Maksimov V. I. , Mordukhovich B. S.

Identyfikatory

DOI

10.1515/amcs-2017-0032

• Języki publikacji: EN

Abstrakty

EN

The paper aims at studying a class of second-order partial differential equations subject to uncertainty involving unknown inputs for which no probabilistic information is available. Developing an approach of feedback control with a model, we derive an efficient reconstruction procedure and thereby design differential equations of reconstruction. A characteristic feature of the obtained equations is that their inputs formed by the feedback control principle constructively approximate unknown inputs of the given second-order distributed parameter system.

Słowa kluczowe

EN

partial differential equation; equations of reconstruction; distributed parameter system

PL

równanie różniczkowe cząstkowe; układ o parametrach rozłożonych; równanie drugiego rzędu

• Wydawca: Oficyna Wydawnicza Uniwersytetu Zielonogórskiego
• Czasopismo: International Journal of Applied Mathematics and Computer Science
• Rocznik: 2017
• Tom: Vol. 27, no. 3
• Strony: 467--475
• Opis fizyczny: Bibliogr. 19 poz., wykr.

Twórcy

autor

Maksimov V. I.

• Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, S. Kovalevskaya 16, Yekaterinburg 620990, Russia; Graduate School of Economics and Management, Ural Federal University, Yekaterinburg 620002, Russia

autor

Mordukhovich B. S.

• Department of Mathematics, Wayne State University, Detroit, MI 48202, USA; Department of Mathematics, RUDN University, Moscow 117198, Russia

Bibliografia

• [1] Banks, H.T. and Kunisch, K. (1980). Estimation Techniques for Distributed Parameter Systems, Birkhäuser, Boston, MA.
• [2] Barbashin, E.A. (1970). Introduction to the Theory of Stability, Wolters/Noordhoff, Groningen.
• [3] Gajewski, H., Groger, K. and Zacharias, K. (1974). Nichtlineare operatorgleichungen und operator differentialgleichungen, Academic Verlag, Berlin.
• [4] Krasovskii, N.N. and Subbotin, A.I. (1988). Game-Theoretial Control Problems, Springer Verlag, New York, NY/Berlin.
• [5] Kryazhimskii, A.V. and Osipov, Yu.S. (1995). Inverse Problems for Ordinary Differential Equations: Dynamical Solutions, Gordon and Breach, London.
• [6] Kryazhimskii, A.V. and Maksimov, V.I. (2010). Resource-saving infinite-horizon tracking under uncertain input, Applied Mathematics and Computations 217(3): 1135–1140.
• [7] Kapustyan, V. and Maksimov, V. (2014). On attaining the prescribed quality of a controlled fourth order system, International Journal of Applied Mathematics and Computer Science 24(1): 75–85, DOI: 10.2478/amcs-2014-0006.
• [8] Lasiecka, I., Triggiani, R. and Yao, P.-F. (1999). Inverse/observability estimates for second order hyperbolic equations with variable coefficients, Journal of Mathematical Analysis and Applications 235(1): 13–57.
• [9] Lavrentiev, M.M., Romanov, V.G. and Shishatskii, S.P. (1980). Ill-Posed Problems of Mathematical Physics and Analysis, Nauka, Novosibirsk, (in Russian).
• [10] Maksimov, V.I. (1995). Approximation of an inverse problem for variational inequalities, Differential and Integral Equations 8(8): 2189–2196.
• [11] Maksimov, V.I. (1996). Some dynamical inverse problems for hyperbolic systems, Control and Cybernetics 25(3): 465–481.
• [12] Maksimov, V.I. and Pandolfi, L. (2001). The reconstruction of unbounded controls in non-linear dynamical systems, Journal of Applied Mathematics and Mechanics 65(3): 371–380.
• [13] Maksimov, V.I. (2002). Dynamics Inverse Problems of Distributed Systems, VSP, Utrecht/Boston, MA.
• [14] Maksimov, V.I. and Tröltzsch, F. (2006). Dynamical state and control reconstruction for a phase field model, Dynamics of Continuous, Discrete and Impulsive Systems A: Mathematical Analysis 13(3–4): 419–436.
• [15] Mordukhovich, B.S. and Zhang, K. (1997). Minimax control of parabolic equations with Dirichlet boundary conditions and state constraints, Applied Mathematics and Optimization 36(3): 323–360.
• [16] Mordukhovich, B.S. (2008). Optimization and feedback design of state-constrained parabolic systems, Pacific Journal of Optimization 4(3): 549–570.
• [17] Mordukhovich, B.S. (2011). Optimal control and feedback design of state-constrained parabolic systems in uncertainty conditions, Applicable Analysis 90(6): 1075–1109.
• [18] Schwaller, B., Ensminger, D., Dresp-Langley, B. and Ragot, J. (2013). State estimation for a class of nonlinear systems, International Journal of Applied Mathematics and Computer Science 23(2): 383–394, DOI: 10.2478/amcs-2013-0029.
• [19] Warga, J. (1972). Optimal Control of Differential and Functional Equations, Academic Press, New York, NY.

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).