Opuscula Math. 34, no. 4 (2014), 763-775
http://dx.doi.org/10.7494/OpMath.2014.34.4.763

 
Opuscula Mathematica

Optimization of a fractional Mayer problem - existence of solutions, maximum principle, gradient methods

Dariusz Idczak
Stanislaw Walczak

Abstract. In the paper, we study a linear-quadratic optimal control problem of Mayer type given by a fractional control system. First, we prove a theorem on the existence of a solution to such a problem. Next, using the local implicit function theorem, we derive a formula for the gradient of a cost functional under constraints given by a control system and prove a maximum principle in the case of a control constraint set. The formula for the gradient is used to implement the gradient methods for the problem under consideration.

Keywords: fractional Riemann-Liouville derivative, Mayer problem, existence of an optimal solution, maximum principle, gradient method.

Mathematics Subject Classification: 26A33, 49J15, 49K15, 49M37.

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  • Dariusz Idczak
  • Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland
  • Stanislaw Walczak
  • Faculty of Mathematics and Computer Science, University of Lodz, Banacha 22, 90-238 Lodz, Poland
  • Received: 2014-01-27.
  • Revised: 2014-10-14.
  • Accepted: 2014-10-14.
Opuscula Mathematica - cover

Cite this article as:
Dariusz Idczak, Stanislaw Walczak, Optimization of a fractional Mayer problem - existence of solutions, maximum principle, gradient methods, Opuscula Math. 34, no. 4 (2014), 763-775, http://dx.doi.org/10.7494/OpMath.2014.34.4.763

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