A numerical optimal control method for solving a large thermic process
RAIRO - Operations Research - Recherche Opérationnelle, Volume 50 (2016) no. 2, pp. 297-314.

This work deals with the optimal regulation of a large thermal process when the final state is fixed and the control is subject to some constraints, for which we propose a relaxation method coupled with the shooting one. We study the behavior of this method. The studied example concerns the optimal control law for two ovens with three and twelve heating zones.

Received:
Accepted:
DOI: 10.1051/ro/2015018
Classification: 34H05, 34K35, 65Kxx
Keywords: Optimal control, relaxation method, shooting method, sub-differential, thermic process
Kara, Fadila 1; Spiteri, Pierre 2; Messine, Frederic 3; Mohamed, Aidene 1

1 Laboratoire de Conception et Conduite de Systèmes de Production (L2CSP), Tizi-Ouzou, Algeria.
2 IRIT-ENSEEIHT, Université de Toulouse, France.
3 LAPLACE-ENSEEIHT, Université de Toulouse, France.
@article{RO_2016__50_2_297_0,
     author = {Kara, Fadila and Spiteri, Pierre and Messine, Frederic and Mohamed, Aidene},
     title = {A numerical optimal control method for solving a large thermic process},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {297--314},
     publisher = {EDP-Sciences},
     volume = {50},
     number = {2},
     year = {2016},
     doi = {10.1051/ro/2015018},
     mrnumber = {3479870},
     zbl = {1338.49058},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/ro/2015018/}
}
TY  - JOUR
AU  - Kara, Fadila
AU  - Spiteri, Pierre
AU  - Messine, Frederic
AU  - Mohamed, Aidene
TI  - A numerical optimal control method for solving a large thermic process
JO  - RAIRO - Operations Research - Recherche Opérationnelle
PY  - 2016
SP  - 297
EP  - 314
VL  - 50
IS  - 2
PB  - EDP-Sciences
UR  - http://archive.numdam.org/articles/10.1051/ro/2015018/
DO  - 10.1051/ro/2015018
LA  - en
ID  - RO_2016__50_2_297_0
ER  - 
%0 Journal Article
%A Kara, Fadila
%A Spiteri, Pierre
%A Messine, Frederic
%A Mohamed, Aidene
%T A numerical optimal control method for solving a large thermic process
%J RAIRO - Operations Research - Recherche Opérationnelle
%D 2016
%P 297-314
%V 50
%N 2
%I EDP-Sciences
%U http://archive.numdam.org/articles/10.1051/ro/2015018/
%R 10.1051/ro/2015018
%G en
%F RO_2016__50_2_297_0
Kara, Fadila; Spiteri, Pierre; Messine, Frederic; Mohamed, Aidene. A numerical optimal control method for solving a large thermic process. RAIRO - Operations Research - Recherche Opérationnelle, Volume 50 (2016) no. 2, pp. 297-314. doi : 10.1051/ro/2015018. http://archive.numdam.org/articles/10.1051/ro/2015018/

V. Barbu, Nonlinear Semigroups and Differential Equations in Banach Spaces. Noordhoff International Publishing (1976). | MR | Zbl

N. Cheik-Obeid, A.W. EL Awtani, B. Lang and P. Spiteri, Decentralized Calculations in Optimal Control of a Large Thermic Process: Method and Results. Proc. of the International Conference of Large Scale Systems. Pergamon Press (1981) 505–516.

D. Gien, B. Lang, J.C. Miellou, L. Raffort and P. Spiteri, Commande optimale de systèmes complexes. RAIRO Autom. Syst. Anal. Control 18 (1984) 209–224. | MR | Zbl

P.J. Laurent, Approximation et Optimisation. Collection Enseignement des Sciences (1972). | MR | Zbl

B. Lang, J.C. Miellou and P. Spiteri, Asynchronous relaxation algorithms for optimal control problems. Math. Comput. Simul. 28 (1986) 227–242. | DOI

B. Lang and P. Spiteri, Decomposition and Coordination Using Asynchronous Iterations. Encyclopedia of Systems and Control, edited by M. Singh. Pergamon Press (1987) 3475−3481.

F. Lhote, J.C. Miellou, B. Lang and P. Spiteri, Relaxation Methods of Parallel in Line Calculations of the Optimum Control of Large Systems, Optimizations Techniques, part I. Springer-Verlag (1980) 324-330. | MR | Zbl

J.C. Miellou and P. Spiteri, A Parallel Asynchronous Relaxation Algorithm for Optimal Control Problems. Proc. of the Int. Conf. Math. Anal. Appl. Kuwait (1985). | Zbl

J.M. Ortega and W.C. Rheinboldt, Iterative Solution of Nonlinear Equations in Several Variables. Academic Press, New York (1970). | MR | Zbl

E. Trélat, Contrôle Optimal: Théorie et Applications. Vuibert, collection Mathématiques Concrètes (2005). | MR | Zbl

Cited by Sources: