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Asymptotical stability of optimal paths in nonconvex problems

In: Optimization

Author

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  • Musa A. Mamedov

    (University of Ballarat)

Abstract

In this chapter we study the turnpike property for the nonconvex optimal control problems described by the differential inclusion $$\dot{x} \in a(x)$$ . We study the infinite horizon problem of maximizing the functional $$\int_{0}^{T} u(x(t))\,dt$$ as T grows to infinity. The purpose of this chapter is to avoid the convexity conditions usually assumed in turnpike theory. A turnpike theorem is proved in which the main conditions are imposed on the mapping a and the function u. It is shown that these conditions may hold for mappings a with nonconvex images and for nonconcave functions u.

Suggested Citation

  • Musa A. Mamedov, 2009. "Asymptotical stability of optimal paths in nonconvex problems," Springer Optimization and Its Applications, in: Charles Pearce & Emma Hunt (ed.), Optimization, edition 1, chapter 0, pages 95-134, Springer.
    • Handle: RePEc:spr:spochp:978-0-387-98096-6_5
    DOI: 10.1007/978-0-387-98096-6_5
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    Cited by:

    1. Vassili Kolokoltsov & Wei Yang, 2012. "Turnpike Theorems for Markov Games," Dynamic Games and Applications, Springer, vol. 2(3), pages 294-312, September.
    2. Anatoli Ivanov & Musa Mammadov & Sergei Trofimchuk, 2013. "Global stabilization in nonlinear discrete systems with time-delay," Journal of Global Optimization, Springer, vol. 56(2), pages 251-263, June.

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