Abstract
In this article, we solve the time minimal control problem of a batch reactor in which three species X, Y, Z are reacting according to the scheme X ↦ Y ↦ Z and every reaction in the sequence obeys first order kinetics. The control variable is the temperature in the batch and the terminal condition is a specified ratio of concentrations of species X and Y. The optimal law is computed using Pontryagin’s Maximum Principle as a synthesis function.
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Références
B.Bonnard “Feedback equivalence for non linear Systems and the time optimal control problem”, to appear in SIAM J. on control and optimization.
B.Bonnard, I.Kupka “Théorie des singularités de l’application entrée/sortie et optimalité des trajectoires singulières dans le problème du temps minimal”, to appear.
C.G.Hill “An introduction to chemical engineering kinetics and reactor design” John Wiley and Sons”, New York, 1977.
I.Kupka “Geometric theory of extremals in optimal control problems: I-The fold and Maxwell cases” TAMS, vol 299, n° 1, Janvier 1987, 225–243.
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© 1991 Birkhäuser Boston
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Bonnard, B., Gauthier, J.P., de Morant, J. (1991). Geometric Time Optimal Control in Batch Reactors. In: Bonnard, B., Bride, B., Gauthier, JP., Kupka, I. (eds) Analysis of Controlled Dynamical Systems. Progress in Systems and Control Theory, vol 8. Birkhäuser Boston. https://doi.org/10.1007/978-1-4612-3214-8_7
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DOI: https://doi.org/10.1007/978-1-4612-3214-8_7
Publisher Name: Birkhäuser Boston
Print ISBN: 978-1-4612-7835-1
Online ISBN: 978-1-4612-3214-8
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