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Time-Optimal Boundary Control of an Infinite Order Parabolic System with Time Lags

International Journal of Applied Mathematics and Computer Science's Cover Image
International Journal of Applied Mathematics and Computer Science
Selected Topics in Biological Cybernetics (special section, pp. 117 - 170), Andrzej Kasiński and Filip Ponulak (Eds.)

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Choquet, G. (1969). Lectures on Analysis, Vol. 2, W.A. Benjamin, New York.Search in Google Scholar

Dubinskii, J. A. (1975). Sobolev spaces of infinite order and behavior of solution of some boundary value problems with unbounded increase of the order of the equation, Matiematiczeskii Sbornik 98: 163-184, (in Russian).Search in Google Scholar

Dubinskii, J. A. (1976). Non-trivality of Sobolev spaces of infinite order for a full Euclidean space and a torus, Matiematiczeskii Sbornik 100: 436-446, (in Russian).Search in Google Scholar

Dubinskii, J. A. (1981). About one method for solving partial differential equations, Doklady Akademii Nauk SSSR 258: 780-784, (in Russian).Search in Google Scholar

Dunford, N. and Schwartz, J. (1958). Linear Operators, Vol. 1, John Wiley and Sons, New York.Search in Google Scholar

El-Saify, H. A. (2005). Optimal control of n x n parabolic lag system involving time lag, IMA Journal of Mathematical Control and Information 22(3): 240-250.10.1093/imamci/dni011Search in Google Scholar

El-Saify, H. A. (2006). Optimal boundary control problem for n x n infinite order parabolic lag system, IMA Journal of Mathematical Control and Information 23(4): 433-445.10.1093/imamci/dni065Search in Google Scholar

Knowles, G. (1978). Time optimal control of parabolic systems with boundary conditions involving time delays, Journal of Optimization Theory and Applications 25(4): 563-574.10.1007/BF00933521Search in Google Scholar

Kowalewski, A. (1988). Boundary control of distributed parabolic system with boundary condition involving a time-varying lag, International Journal of Control 48(6): 2233-2248.10.1080/00207178808906327Search in Google Scholar

Kowalewski, A. (1990a). Feedback control for a distributed parabolic system with boundary condition involving a timevarying lag, IMA Journal of Mathematical Control and Information 7(2): 143-157.10.1093/imamci/7.2.143Search in Google Scholar

Kowalewski, A. (1990b). Optimal control of distributed parabolic systems involving time lags, IMA Journal of Mathematical Control and Information 7(4): 375-393.10.1093/imamci/7.4.375Search in Google Scholar

Kowalewski, A. (1993). Optimal control of parabolic systems with time-varying lags, IMA Journal of Mathematical Control and Information 10(2): 113-129.10.1093/imamci/10.2.113Search in Google Scholar

Kowalewski, A. (1998). Optimal control of distributed parabolic systems with multiple time-varying lags, International Journal of Control 69(3): 361-381.10.1080/002071798222712Search in Google Scholar

Kowalewski, A. (1999). Optimization of parabolic systems with deviating arguments, International Journal of Control 72(11): 947-959.10.1080/002071799220498Search in Google Scholar

Kowalewski, A. (2001). Optimal Control of Infinite Dimensional Distributed Parameter Systems with Delays, University of Mining and Metallurgy Press, Cracow.Search in Google Scholar

Kowalewski, A. and Duda, J. (1992). 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): 131-146.10.1093/imamci/9.2.131Search in Google Scholar

Kowalewski, A. and Krakowiak, A. (1994). Time-optimal control of parabolic time lag system, AppliedMathematics and Computer Science 4(1): 19-28.Search in Google Scholar

Kowalewski, A. and Krakowiak, A. (2000). Time-optimal control of parabolic system with time lags given in the integral form, IMA Journal of Mathematical Control and Information 17(3): 209-225.10.1093/imamci/17.3.209Search in Google Scholar

Kowalewski, A. and Krakowiak, A. (2006). Time-optimal boundary control of a parabolic system with time lags given in the integral form, International Journal of Applied Mathematics and Computer Science 16(3): 287-295.Search in Google Scholar

Lions, J. (1971). Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, Berlin-Heidelberg.10.1007/978-3-642-65024-6Search in Google Scholar

Lions, J. and Magenes, E. (1972). Non-Homogeneous Boundary Value Problems and Applications, Vols. 1 and 2, Springer-Verlag, Berlin-Heidelberg.Search in Google Scholar

Wang, P. K. C. (1975). Optimal control of parabolic systems with boundary conditions involving time delays, SIAM Journal on Control 13(2): 274-293.10.1137/0313016Search in Google Scholar

ISSN:
1641-876X
Language:
English
Publication timeframe:
4 times per year
Journal Subjects:
Mathematics, Applied Mathematics