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Infinite Horizon Optimal Control pp 156–179Cite as

Existence of Overtaking Optimal Solutions for Nonautonomous Control Systems

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Part of the book series: Lecture Notes in Economics and Mathematical Systems ((LNE,volume 290))

Abstract

In Chapter 4 it was seen that combining the turnpike properties given by Lemma 4.6 with the existence of a strongly optimal solution for the associated problem of Lagrange permitted us to give an existence theory for overtaking optimal solutions. These results utilized strong convexity and compactness hypotheses and moreover were valid only for autonomous systems. In this chapter, by proceeding along the same lines, we will make use of the results of the previous chapter thereby obtaining analogous results for nonautonomous systems where we have, in addition, assumed weaker convexity and compactness hypotheses. Examples 7.1 to 7.3 motivate the developments given below as these models cannot be addressed by the previous theorems.

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Authors and Affiliations

  1. Department of Mathematics, Southern Illinois University at Carbondale, 62901, Carbondale, Illinois, USA

    D. A. Carlson

  2. École des Hautes Études Commerciales, 5255 Avenue Decelles, H3T 1V6, Montréal, QC, Canada

    A. Haurie

  3. École Polytechnique de Montréal, H3C 3A7, Montréal, QC, Canada

    A. Haurie

Authors
  1. D. A. Carlson
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  2. A. Haurie
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© 1987 Springer-Verlag Berlin Heidelberg

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Carlson, D.A., Haurie, A. (1987). Existence of Overtaking Optimal Solutions for Nonautonomous Control Systems. In: Infinite Horizon Optimal Control. Lecture Notes in Economics and Mathematical Systems, vol 290. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-02529-1_7

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  • DOI: https://doi.org/10.1007/978-3-662-02529-1_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-17824-8

  • Online ISBN: 978-3-662-02529-1

  • eBook Packages: Springer Book Archive

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