Differential stability of solutions to air quality control problems in urban area

Piotr Holnicki; Jan Sokołowski; Antoni Żochowski

Aplikace matematiky (1987)

  • Volume: 32, Issue: 3, page 240-253
  • ISSN: 0862-7940

Abstract

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The convex optimal control problem for a system described by the parabolic equation is considered. The form of the right derivative of an optimal solution with respect to the parameter is derived. The applications to an air quality control problem are discussed. Numerical result are provided.

How to cite

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Holnicki, Piotr, Sokołowski, Jan, and Żochowski, Antoni. "Differential stability of solutions to air quality control problems in urban area." Aplikace matematiky 32.3 (1987): 240-253. <http://eudml.org/doc/15496>.

@article{Holnicki1987,
abstract = {The convex optimal control problem for a system described by the parabolic equation is considered. The form of the right derivative of an optimal solution with respect to the parameter is derived. The applications to an air quality control problem are discussed. Numerical result are provided.},
author = {Holnicki, Piotr, Sokołowski, Jan, Żochowski, Antoni},
journal = {Aplikace matematiky},
keywords = {convex optimal control; parabolic equation; air quality control; differential stability; convex optimal control; parabolic equation; air quality control},
language = {eng},
number = {3},
pages = {240-253},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Differential stability of solutions to air quality control problems in urban area},
url = {http://eudml.org/doc/15496},
volume = {32},
year = {1987},
}

TY - JOUR
AU - Holnicki, Piotr
AU - Sokołowski, Jan
AU - Żochowski, Antoni
TI - Differential stability of solutions to air quality control problems in urban area
JO - Aplikace matematiky
PY - 1987
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 32
IS - 3
SP - 240
EP - 253
AB - The convex optimal control problem for a system described by the parabolic equation is considered. The form of the right derivative of an optimal solution with respect to the parameter is derived. The applications to an air quality control problem are discussed. Numerical result are provided.
LA - eng
KW - convex optimal control; parabolic equation; air quality control; differential stability; convex optimal control; parabolic equation; air quality control
UR - http://eudml.org/doc/15496
ER -

References

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  1. Mathematical Models for Planning and Controlling Air Quality, G. Fronza, P. Melli (eds.), Proceedings of IIASA Workshop, Pergamon Press, 1982. (1982) 
  2. P. Holnicki, al., An urban-scale computer model for short-term prediction of air pollution, Arch. Autom. i Telemech, 1 - 2 (1986), 51 - 71. (1986) Zbl0608.90012
  3. P. Holnicki A. Žochowski, Numerical methods in forecasting and controlling air pollution problems, Systems Research Institute, Report No. ZTS-15-7/84, Warsaw, 1984 (in Polish). (1984) 
  4. J. L. Lions, Controle optimal de systemes gouvernes par des equations aux derivees partielles, Dunod, Paris, 1968. (1968) Zbl0179.41801MR0244606
  5. K. Malanowski J. Sokolowski, Sensitivity of solutions to convex control constrained optimal control problems for distributed parameter systems, Journal of Mathematical Analysis and Applications (to appear). Zbl0607.49016MR0861917
  6. G. I. Martchuk, Mathematical Modelling in Enviromental Problems, Nauka, Moscow 1982 (in Russian). (1982) 
  7. B. N. Pshenitchny, Linearization Method, Nauka, Moscow 1983 (in Russian). (1983) 
  8. J. Sokolowski, Sensitivity analysis of control constrained optimal control problems for distributed parameter systems, (submitted). Zbl0647.49019
  9. J. Sokolowski, 10.1007/BF01442201, Applied Mathematics and Optimization, 13 (1985), 97-115. (1985) Zbl0572.49012MR0794173DOI10.1007/BF01442201
  10. J. Sokolowski, Differential stability of control constrained optimal control problems for distributed parameter systems, Proceedings of 2nd International Conference on Control Theory for Distributed Parameter Systems and Applications, Springer Verlag, 331 - 339. Zbl0578.49021MR0897570
  11. J. Sokolowski, Sensitivity Analysis and Parametric Optimization of Optimal Control Problems for Distributed Parameter Systems, Zeszyty Naukowe Politechniki Warszawskiej, seria Elektronika (to appear). Zbl0647.49019
  12. J. Sokolowski, Differential stability of solutions to boundary optimal control problems for parabolic systems, (to appear). Zbl0608.49017
  13. P. Holnicki J. Sokolowski A. Žochowski, Sensitivity analysis of an optimal control problem arising from air quality control in urban area, Proceedings of 11th IFIP Conference on Systems Modelling and Optimization, Budapest, 1985, Springer Verlag, 331 - 339. (1985) Zbl0631.49013MR0903493

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