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

Adam Kowalewski; Anna Krakowiak

International Journal of Applied Mathematics and Computer Science (2008)

- Volume: 18, Issue: 2, page 189-198
- ISSN: 1641-876X

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topAdam Kowalewski, and Anna Krakowiak. "Time-optimal boundary control of an infinite order parabolic system with time lags." International Journal of Applied Mathematics and Computer Science 18.2 (2008): 189-198. <http://eudml.org/doc/207876>.

@article{AdamKowalewski2008,

abstract = {In this paper the time-optimal boundary control problem is presented for a distributed infinite order parabolic system in which time lags appear in the integral form both in the state equation and in the boundary condition. Some specific properties of the optimal control are discussed.},

author = {Adam Kowalewski, Anna Krakowiak},

journal = {International Journal of Applied Mathematics and Computer Science},

keywords = {time-optimal boundary control; infinite order; parabolic system; time lags},

language = {eng},

number = {2},

pages = {189-198},

title = {Time-optimal boundary control of an infinite order parabolic system with time lags},

url = {http://eudml.org/doc/207876},

volume = {18},

year = {2008},

}

TY - JOUR

AU - Adam Kowalewski

AU - Anna Krakowiak

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

JO - International Journal of Applied Mathematics and Computer Science

PY - 2008

VL - 18

IS - 2

SP - 189

EP - 198

AB - In this paper the time-optimal boundary control problem is presented for a distributed infinite order parabolic system in which time lags appear in the integral form both in the state equation and in the boundary condition. Some specific properties of the optimal control are discussed.

LA - eng

KW - time-optimal boundary control; infinite order; parabolic system; time lags

UR - http://eudml.org/doc/207876

ER -

## References

top- Choquet, G. (1969). Lectures on Analysis, Vol.2, W.A. Benjamin, New York. Zbl0181.39602
- 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).
- 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).
- Dubinskii, J. A. (1981). About one method for solving partial differential equations, Doklady Akademii Nauk SSSR 258: 780-784, (in Russian).
- Dunford, N. and Schwartz, J. (1958). Linear Operators, Vol. 1, John Wiley and Sons, New York. Zbl0084.10402
- 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
- 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
- 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
- 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
- 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
- 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
- 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
- Kowalewski, A. (1998). Optimal control of distributed parabolic systems with multiple time-varying lags, International Journal of Control 69(3): 361-381. Zbl0942.49005
- Kowalewski, A. (1999). Optimization of parabolic systems with deviating arguments, International Journal of Control 72(11): 947-959. Zbl0980.49005
- Kowalewski, A. (2001). Optimal Control of Infinite Dimensional Distributed Parameter Systems with Delays, University of Mining and Metallurgy Press, Cracow.
- 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
- 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
- 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
- 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
- Lions, J. (1971). Optimal Control of Systems Governed by Partial Differential Equations, Springer-Verlag, BerlinHeidelberg. Zbl0203.09001
- Lions, J. and Magenes, E. (1972). Non-Homogeneous Boundary Value Problems and Applications, Vols. 1 and 2, Springer-Verlag, Berlin-Heidelberg. Zbl0223.35039
- 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

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