Have a personal or library account? Click to login
Time-optimal control of infinite order hyperbolic systems with time delays Cover

Time-optimal control of infinite order hyperbolic systems with time delays

By: Adam Kowalewski  
Open Access
|Dec 2009

References

  1. Casting, C. (1967). Sur les multi-applications measurables, Revue Francaise d'Informatique et de Recherche Operationelle 1: 91-126.10.1051/m2an/1967010100911
  2. Choquet, G. (1969). Lectures on Analysis, Vol. 2, W.A. Benjamin, New York, NY.
  3. Dubinskij, 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.
  4. Dubinskij, J. A. (1976). Non-trivality of Sobolev spaces of infinite order for a full euclidean space and a torus, Matiematiczeskii Sbornik 100: 436-446.
  5. Dubinskij, J. A. (1986). Sobolev Spaces of Infinite Order and Differential Equations, Teubner-Texte zur Mathematik, Vol. 87, Teubner-Verlag, Leipzig.
  6. Dunford, N. and Schwartz, J. (1958). Linear Operators, Vol. 1, John Wiley and Sons, New York, NY.
  7. El-Saify, H. A. and Bahaa, G. M. (2002). Optimal control for n x n hyperbolic systems involving operators of infinite order, Mathematica Slovaca 52: 409-422.
  8. Friedman, A. (1969). Partial Differential Equations, Holt, Reinhart and Winston, New York, NY.
  9. 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/BF00933521
  10. Kowalewski, A. (1993a). Boundary control of hyperbolic system with time lags, IMA Journal of Mathematical Control and Information 10: 261-272.10.1093/imamci/10.3.261
  11. Kowalewski, A. (1993b). Optimal control of hyperbolic system with time lags, Applied Mathematics and Computer Science 3(4): 687-697.
  12. Kowalewski, A. (1995). Optimal control of hyperbolic system with time-varying lags, IMA Journal of Mathematical Control and Information 12: 133-143.10.1093/imamci/12.2.133
  13. Kowalewski, A. (1998). Optimal control of a distributed hyperbolic system with multiple time-varying lags, International Journal of Control 71: 419-435.10.1080/002071798221759
  14. Kowalewski, A. (2000). Optimal control of distributed hyperbolic systems with deviating arguments, International Journal of Control 73: 1026-1041.10.1080/002071700411313
  15. Kowalewski, A. (2003). Time-optimal control problem of hyperbolic systems with deviating arguments, International Journal of Control 76: 557-565.10.1080/0020717031000079472
  16. Lions, J. (1971). Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, Berlin/Heidelberg.10.1007/978-3-642-65024-6
  17. Lions, J. and Magenes, E. (1972). Non-Homogeneous Boundary Value Problems and Applications, Vols. 1 and 2, Springer-Verlag, Berlin/Heidelberg.
  18. Olech, C. (1966). Extremal solutions of a control system, Journal of Differential Equations 2: 74-101.10.1016/0022-0396(66)90064-7
  19. Tanabe, H. (1965). On differentiability and analyticity of weighted elliptic boundary-value problems, Osaka Mathematical Journal 2: 163-190.
  20. Wang, P. K. C. (1975). Optimal control of parabolic systems with boundary conditions involving time delays, SIAM Journal of Control 13(2): 274-293.10.1137/0313016
DOI: https://doi.org/10.2478/v10006-009-0047-x | Journal eISSN: 2083-8492 | Journal ISSN: 1641-876X
Language: English
Page range: 597 - 608
Published on: Dec 31, 2009
Published by: University of Zielona Góra
In partnership with: Paradigm Publishing Services
Publication frequency: 4 issues per year

© 2009 Adam Kowalewski, published by University of Zielona Góra
This work is licensed under the Creative Commons License.

Volume 19 (2009): Issue 4 (December 2009)