Time-optimal boundary control of an infinite order parabolic system with time lags

 Access to full text

 Full (PDF)

1. Choquet, G. (1969). Lectures on Analysis, Vol.2, W.A. Benjamin, New York. Zbl0181.39602
2. 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). 
3. 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). 
4. Dubinskii, J. A. (1981). About one method for solving partial differential equations, Doklady Akademii Nauk SSSR 258: 780-784, (in Russian). 
5. Dunford, N. and Schwartz, J. (1958). Linear Operators, Vol. 1, John Wiley and Sons, New York. Zbl0084.10402
6. El-Saify, H. A. (2005). Optimal control of n × n parabolic lag system involving time lag, IMA Journal of Mathematical Control and Information 22(3): 240-250. Zbl1094.49019
7. El-Saify, H. A. (2006). Optimal boundary control problem for n × n infinite order parabolic lag system, IMA Journal of Mathematical Control and Information 23(4): 433-445. Zbl1113.49023
8. 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. Zbl0368.49007
9. Kowalewski, A. (1988). Boundary control of distributed parabolic system with boundary condition involving a timevarying lag, International Journal of Control 48(6): 2233-2248. Zbl0662.49011
10. 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. Zbl0717.49018
11. Kowalewski, A. (1990b). Optimal control of distributed parabolic systems involving time lags, IMA Journal of Mathematical Control and Information 7(4): 375-393. Zbl0721.49022
12. Kowalewski, A. (1993). Optimal control of parabolic systems with time-varying lags, IMA Journal of Mathematical Control and Information 10(2): 113-129. Zbl0874.49021
13. Kowalewski, A. (1998). Optimal control of distributed parabolic systems with multiple time-varying lags, International Journal of Control 69(3): 361-381. Zbl0942.49005
14. Kowalewski, A. (1999). Optimization of parabolic systems with deviating arguments, International Journal of Control 72(11): 947-959. Zbl0980.49005
15. Kowalewski, A. (2001). Optimal Control of Infinite Dimensional Distributed Parameter Systems with Delays, University of Mining and Metallurgy Press, Cracow. 
16. 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. Zbl0767.49002
17. Kowalewski, A. and Krakowiak, A. (1994). Time-optimal control of parabolic time lag system, Applied Mathematics and Computer Science 4(1): 19-28. Zbl0831.49008
18. 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. Zbl0980.49004
19. 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. Zbl1171.49307
20. Lions, J. (1971). Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, BerlinHeidelberg. Zbl0203.09001
21. Lions, J. and Magenes, E. (1972). Non-Homogeneous Boundary Value Problems and Applications, Vols. 1 and 2, Springer-Verlag, Berlin-Heidelberg. Zbl0223.35039
22. Wang, P. K. C. (1975). Optimal control of parabolic systems with boundary conditions involving time delays, SIAM Journal on Control 13(2): 274-293. Zbl0301.49009