Article
MSC:
35K20,
49A50,
49J45,
49K20,
86A35,
92D40,
93B35,
93C20,
93C75,
93D99 | MR 0895881 | Zbl 0631.49013 | DOI: 10.21136/AM.1987.104254
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Keywords:
convex optimal control; parabolic equation; air quality control; differential stability
convex optimal control; parabolic equation; air quality control; differential stability
Summary:
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.
References:
[1] Mathematical Models for Planning and Controlling Air Quality. G. Fronza, P. Melli (eds.), Proceedings of IIASA Workshop, Pergamon Press, 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. Zbl 0608.90012
[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).
[4] J. L. Lions: Controle optimal de systemes gouvernes par des equations aux derivees partielles. Dunod, Paris, 1968. MR 0244606 | Zbl 0179.41801
[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). MR 0861917
[6] G. I. Martchuk: Mathematical Modelling in Enviromental Problems. Nauka, Moscow 1982 (in Russian).
[7] B. N. Pshenitchny: Linearization Method. Nauka, Moscow 1983 (in Russian).
[8] J. Sokolowski: Sensitivity analysis of control constrained optimal control problems for distributed parameter systems. (submitted). Zbl 0647.49019
[9] J. Sokolowski: Differential stability of solutions to constrained optimization problems. Applied Mathematics and Optimization, 13 (1985), 97-115. DOI 10.1007/BF01442201 | MR 0794173 | Zbl 0572.49012
[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. MR 0897570 | Zbl 0578.49021
[11] J. Sokolowski: Sensitivity Analysis and Parametric Optimization of Optimal Control Problems for Distributed Parameter Systems. Zeszyty Naukowe Politechniki Warszawskiej, seria Elektronika (to appear).
[12] J. Sokolowski: Differential stability of solutions to boundary optimal control problems for parabolic systems. (to appear). Zbl 0608.49017
[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. MR 0903493
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