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Optimization of a Fractional Differential Equation

  • Enrique Otárola
  • Abner J. Salgado
Chapter
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 163)

Abstract

We consider a linear quadratic optimization problem where the state is governed by a fractional ordinary differential equation. We also consider control constraints. We show existence and uniqueness of an optimal state–control pair and propose a method to approximate it. Due to the low regularity of the solution to the state equation, rates of convergence cannot be proved unless problematic assumptions are made. Instead, we appeal to the theory of Γ-convergence to show the convergence of our scheme.

Notes

Acknowledgements

E. Otárola was supported in part by CONICYT through FONDECYT project 3160201. A.J. Salgado was supported in part by NSF grant DMS-1418784.

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Authors and Affiliations

  1. 1.Departamento de MatemáticaUniversidad Técnica Federico Santa MaríaValparaísoChile
  2. 2.Department of MathematicsUniversity of TennesseeKnoxvilleUSA

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