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Relaxation methods for parallel in line calculations of the optimum control of large systems

  • Lhote F. 
  • Lang B. 
  • Miellou J. C. 
  • Spiteri P. 
Optimal Control: Ordinary And Delay Differential Equations
Part of the Lecture Notes in Control and Information Sciences book series (LNCIS, volume 22)

Abstract

The optimal regulation with a sliding horizon of complex, linear or non linear, processes necessitates a device which will accomplish in real time the collection of process data, the treatment of in line information, and the action on control variables.

The computing method consists of solving the Hamilton-Pontriaguine equations of the global process by : decomposition into subsystems of equations relative to subprocesses iterative coordination of corresponding subproblems by “delayed chaotic relaxation algorithms”.

These family of methods generalise past works of Takahara and Wismer ; it is shown, in the linear-quadratic case, that the problem can always be coordinated by relaxation when the state matrix is the opposite of an H-matrix, with a suitable penalization of commande error.

A specialized multi-microprocessor computer is under construction at Besançon. For the moment, all trials have been carried out using a hybrid system which consists of a minicomputer associated with a rapid analog integration machine constructed in the laboratory. Comparative results of global and decentralized methods are given for a thermic process example, realized by both monoprocessor systems and parallel (hybrid) system, the latter systems giving very interesting performances compatible with and in line with usage. Thusly the possibility exists of an “intermittently closed loop” command thanks to a calculation made periodically from the real state of the process, in negligeable time comparated to the horizon of the command considered. This system can be superimposed on a pre-existing classical system of regulation, whose presence does not complicate the calculations but constitutes a security (hierarchical command).

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References

  1. [1]
    BAUDET G.M. (1978). Asynchronous iterative method for multiprocessors. A.C.M.Google Scholar
  2. [2]
    CHAZAN D., MIRANKER M. (1969). Chaotic relaxation. Linear algebra ant its appl., Vol. no 2.Google Scholar
  3. [3]
    COMTE P. (1976). Algorithmes de relaxation-décentralisation. 3th cycle thesis. Franche-Comté University.Google Scholar
  4. [4]
    COMTE P., LANG B., LHOTE F., MIELLOU J.C. and SPITERI P. (1975). Algorithmes de relaxation-décentralisation en contrôle optimal. Report A.T.P. CNRS, no 1L9901.Google Scholar
  5. [5]
    EL AWTANI A.W. (1978). Réalisation, identification et commande d'un processus thermique à entrées et sorties multiples. 3th cycle thesis. Franche-Comté University.Google Scholar
  6. [6]
    HENRIOUD J.M., LANG B., LHOTE F. (1976). Hierarchical hybrid computation of optimal control for a composite system. IFAC Symposium on large scale systems — UDINE.Google Scholar
  7. [7]
    LANG B. (1977). Calcul hybride décentralisé de la commande optimale d'un proces sus dynamique continu. Ingenior doctor thesis. Franche-Comté University.Google Scholar
  8. [8]
    LHOTE F., MIELLOU J.C., LANG B. and SPITERI P. (1978). Mise au point d'un système hybride de commande optimale décentralisée. Report A.T.P. CNRS.Google Scholar
  9. [9]
    LIONS J.L. (1968). Contrôle optimal des systèmes gouvernés par des équations aux dérivées partielles. Dunod, Gauthier Villars, Paris.Google Scholar
  10. [10]
    MIELLOU J.C. (1972). Méthode de l'état adjoint par relaxation. RAIRO, No 1, pp. 81–87.Google Scholar
  11. [11]
    MIELLOU J.C. (1973). Problèmes de contrôle optimal H-décentralisable: la méthode de relaxation-décentralisation. CRAS, t. 277, série A, pp. 609–612.Google Scholar
  12. [12]
    MIELLOU J.C. (1975). Algorithmes de relaxation chaotique à retards. RAIRO, pp. 55–82.Google Scholar
  13. [13]
    STOER J. (1975). Quadratic termination and quadratic convergence of minimisation algorithms. Topics in numerical analysis, t. III.Google Scholar
  14. [14]
    TAKAHARA Y. (1964). Multi-level approach to dynamic optimisation — Systems Research Center Report SRC SOC 6418, Case Western, U. Cleveland.Google Scholar
  15. [15]
    TITLI A. and ALL (1979). Algorithmes de décentralisation et de coordination par relaxation en commande optimale. In Cepadues (Ed.), Analyse et commande des systèmes complexes, monographie AFCET.Google Scholar
  16. [16]
    WISMER D.A. (1971). Optimisation methods for large-scale systems. Ch. 6: Distributed multilevel systems. Mac Graw Hill.Google Scholar

Copyright information

© Springer-Verlag 1980

Authors and Affiliations

  • Lhote F. 
    • 1
  • Lang B. 
    • 1
  • Miellou J. C. 
    • 1
  • Spiteri P. 
    • 1
  1. 1.Université de Franche-ComteFrance

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