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Journal of Optimization Theory and Applications

, Volume 67, Issue 2, pp 321–354 | Cite as

Optimal control of nonlinear evolution inclusions

  • N. S. Papageorgiou
Contributed Papers

Abstract

In this paper, we study the optimal control of nonlinear evolution inclusions. First, we prove the existence of admissible trajectories and then we show that the set that they form is relatively sequentially compact and in certain cases sequentially compact in an appropriate function space. Then, with the help of a convexity hypothesis and using Cesari's approach, we solve a general Lagrange optimal control problem. After that, we drop the convexity hypothesis and pass to the relaxed system, for which we prove the existence of optimal controls, we show that it has a value equal to that of the original one, and also we prove that the original trajectories are dense in an appropriate topology to the relaxed ones. Finally, we present an example of a nonlinear parabolic optimal control that illustrates the applicability of our results.

Key Words

Evolution inclusions dense embedding transition probability support functions relaxed systems Caratheodory integrands Arzela-Ascoli theorem monotone operators parabolic systems 

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Copyright information

© Plenum Publishing Corporation 1990

Authors and Affiliations

  • N. S. Papageorgiou
    • 1
  1. 1.Department of Mathematical SciencesNational Technical University of AthensAthensGreece

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