Hostname: page-component-586b7cd67f-2brh9 Total loading time: 0 Render date: 2024-11-24T03:42:14.475Z Has data issue: false hasContentIssue false
  • English
  • Français

Some Applications of Optimal ControlTheory of Distributed Systems

Published online by Cambridge University Press:  15 August 2002

Alfredo Bermudez
Alfredo Bermudez*
Affiliation:
Departamento de Matemática Aplicada, Universidade de Santiago de Compostela, 15706 Santiago de Compostela, Spain; [email protected].
Get access

Abstract

In this paper we present some applications of the J.-L. Lions' optimal control theory to real life problems in engineering and environmental sciences. More precisely, we deal with the following three problems: sterilization of canned foods, optimal management of waste-water treatment plants and noise control

Keywords

Optimal controlsterilizationcanned foodwater pollutionnoise reduction.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 8: A tribute to JL Lions , 2002 , pp. 195 - 218
Copyright
© EDP Sciences, SMAI, 2002

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Álvarez-Vázquez, L. and Martínez, A., Modelling and control of natural convection in canned foods. IMA J. Appl. Math. 63 (1999) 246-265. CrossRef
Baek, K.H. and Elliot, S.J., Natural algorithms for choosing source locations in active control systems. J. Sound Vibr. 186 (1995) 245-267. CrossRef
Beranek and Ver, Noise and vibration control engineering. Principles and applications. John Wiley and Sons, New York (1992).
A. Bermúdez, Mathematical techniques for some environmental problems related to water pollution control, in Mathematics, Climate and Environment, edited by J.I. Díaz, J.-L. Lions. Masson, Paris (1993).
Bermúdez, A. and Martínez, A., A state constrained optimal control problem related to the sterilization of canned foods. Automatica. The IFAC Journal 30 (1994) 319-329. CrossRef
Bermúdez, A., Martínez, A. and Rodríguez, C., Un problème de contrôle ponctuel lié à l'emplacement optimal d'émissaires d'évacuation sous-marine. C. R. Acad. Sci. Paris Sér. I Math. 313 (1991) 515-518.
Bermúdez, A., Rodríguez, C. and Vilar, M.A., Solving shallow water equations by a mixed implicit finite element method. IMA J. Num. Anal. 11 (1991) 79-97. CrossRef
Bermúdez, A. and Saguez, C., Optimal control of a Signorini problem. SIAM J. Control Optim. 25 (1987) 576-582. CrossRef
J.F. Bonnans and E. Casas, Contrôle de systèmes elliptiques semilinéaires comportant des contraintes distribuées sur l'état, in Nonlinear partial differential equations and their applications, edited by H. Brezis and J.-L. Lions. Pitman (1988).
Casas, E., L 2 estimates for the finite element method for the Dirichlet problem with singular data. Numer. Math. 47 (1985) 627-632. CrossRef
Casas, E., Control of an elliptic problem with pointwise state constraints. SIAM J. Control Optim. 24 (1986) 1309-1318. CrossRef
Casas, E., Pontryagin's principle for state constrained boundary control problems of semilinear parabolic equations. SIAM J. Control Optim. 35 (1997) 1297-1327. CrossRef
Bonnans, J.F., An introduction to Newton type algorithms for nonlinearly constrained optimization problems. Birkhauser-Verlag, Basel, Internat. Ser. Numer. Math. 87 (1989) 1-17.
E. Casas and C. Pola , PLCBAS User's Guide VERSION 1.1. Computación 1. Universidad de Cantabria, Santander, Spain (1989).
P.G. Ciarlet, Basic error estimates for elliptic problems, in Handbook of Numerical Analysys, Vol. II, edited by P.G. Ciarlet and J.-L. Lions. North-Holand (1991).
Di Benedetto, E., On the local behaviour of solutions of degenerate parabolic equatons with measurable coefficients. Ann. Scuola Norm. Sup. Pisa Cl. Sci. 13 (1986) 487-535.
I. Ekeland and R. Temam, Convex analysis and variational problems. North-Holland, Amsterdam (1976).
P. Gamallo, Contribución al estudio matemático de problemas de simulación y control activo del ruido, Ph. Thesis. Universidade de Santiago de Compostela, Spain (2002).
Herskovits, J., A two stage feasible directions algorithm for nonlinear constrained optimization. Math. Programming 36 (1986) 19-38. CrossRef
Herskovits, J., A feasible directions interior point technique for nonlinear optimization. J. Optim. Theory Appl. 99 (1998) 121-146. CrossRef
J.B. Hiriart-Urruty and C. Lemarechal, Convex analysis and Minimization Algorithms. Springer-Verlag, Berlin, Heildelberg (1993).
Hu, B. and Yong, J., Pontriagin maximum principle for semilinear and quasilinear parabolic equations with pointwise state constraints. SIAM J. Control Optim. 33 (1995) 1857-1880. CrossRef
O.A. Ladyzhenskaya, V.A. Solonnikov and N.N. Uraltseva, Linear and quasilinear equations of parabolic type. Amer. Math. Soc., Providence, Transl. Math. Monogr. 23 (1968).
J.-L. Lions, Contrôle optimal de systèmes gouvernés par des équations aux dérivées partielles. Dunod, Paris (1968).
J.-L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires. Dunod, Paris (1969).
P.A. Nelson and S.J. Elliot, Active Control of Sound. Academic Press, London (1999).
G.I. Marchuk, Mathematical models in environmental problems. North Holland, Amsterdam (1986).
Martínez, A., Rodríguez, C. and Vázquez-Méndez, M.E., Theoretical and numerical analysis of an optimal control problem related to waste-water treatment. SIAM J. Control Optim. 38 (2000) 1534-1553. CrossRef
C. Olin Ball and F.C.W. Olson, Sterilization in food technology. Mc Graw Hill, New York (1957).
R.I. Pérez Martín, J.R. Banga and J.M. Gallardo, Simulation of thermal processes in tuna can manufacture. Instituto de Investigaciones Marinas (C.S.I.C.), Vigo, Spain (1989).
Panier, E.R., Tits, A.L. and Herskovits, J., QP-Free, A, Globally Convergent, Locally Superlinearly Convergent Algorithm for Inequality Constrained Optimization. SIAM J. Control Optim. 26 (1988) 788-810. CrossRef
Scott, R., Finite element convergence for singular data. Numer. Math. 21 (1973) 317-327. CrossRef
M.E. Vázquez-Méndez, Contribución a la resolución numérica de modelos para el estudio de la contaminación de aguas. Master thesis. Dept. Matemática Aplicada. Univ. Santiago de Compostela, Spain (1992).