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On an optimization problem with cost of rapid variation of control

Published online by Cambridge University Press:  17 February 2009

D. Idczak ,
K. Kibalczyc  and
S. Walczak
D. Idczak
Affiliation:
Institute of Mathematics, Lódź University, ul. Stefana Banacha 22, 90–238 Lódź, Poland
K. Kibalczyc
Affiliation:
Institute of Mathematics, Lódź University, ul. Stefana Banacha 22, 90–238 Lódź, Poland
S. Walczak
Affiliation:
Institute of Mathematics, Lódź University, ul. Stefana Banacha 22, 90–238 Lódź, Poland
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Abstract

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In the paper we give sufficient conditions for the existence of a solution for a Darboux-Goursat optimization problem with a cost functional depending on the number of switchings of a control and the rapidity of its changes. An application is given to a gas absorption problem.

Type
Research Article
Information
The ANZIAM Journal , Volume 36 , Issue 1 , July 1994 , pp. 117 - 131
Copyright
Copyright © Australian Mathematical Society 1994

References

[1]Bielecki, A., “Une remarque sur l'application de la méthode de Banach-Cocciopoli-Tichonov dans la théorie de l'équation s = f(x, y, z, p, q)”, Bull. Acad. Pol. Sci. 4 (1956) 265–268.Google Scholar
[2]Blatt, J. M., “Optimal control with a cost of switching control”, J. Austral. Math. Soc. Ser. B 19 (1976) 316–332.Google Scholar
[3]Cesari, L., Optimization - Theory and applications (Springer-Verlag, New York, 1983).CrossRefGoogle Scholar
[4]Kibalczyc, K. and Walczak, S., “Necessary optimality conditions for a problem with cost of rapid variation of control”, J. Austral. Math. Soc. Ser. B 26 (1984) 45–55.Google Scholar
[5]Krasnosielski, M. A., Topological methods in the theory of nonlinear integral equations (Macmillan, New York, 1964).Google Scholar
[6]Lojasiewicz, S., An introduction to the theory of real functions (John Willey and Sons, Chichester, 1988).Google Scholar
[7]Matula, J., “On an extremum problem”, J. Austral. Math. Soc. Ser. B 28 (1987) 376–392.CrossRefGoogle Scholar
[8]Noussair, E. S., “On the existence of piecewise continuous optimal controls”, J. Austral. Math. Soc. Ser. B 20 (1977) 31–37.CrossRefGoogle Scholar
[9]Saks, S., Theory of the integral (Warsaw, 1937).Google Scholar
[10]Stewart, D. E., “A numerical algorithm for optimal control problems with switching costs”, J. Austral. Math. Soc. Ser. B 34 (1992) 212–228.Google Scholar
[11]Teo, K. L. and Jennings, L. S., “Optimal control with a cost on changing control”, J. Optim. Theory Appl. 68 (2) (1991) 335–357.CrossRefGoogle Scholar
[12]Tikhonov, A. N. and Samarski, A. A., Equations of mathematical physics (Moscow, 1978).Google Scholar
[13]Walczak, S., “Absolutely continuous functions of several variables and their applications to differential equations”, Bull. Polish Acad. Sci. Math. 35 (11–12) (1987) 733–744.Google Scholar
[14]Walczak, S., “On the differentiability of absolutely continuous functions of several variables”, Bull. Polish Acad. Sci. Math. 36 (9–10) (1988) 513–520.Google Scholar