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Optimal Control of the Fokker–Planck Equation with Space-Dependent Controls

Author

Listed:
  • Arthur Fleig

    (University of Bayreuth)

  • Roberto Guglielmi

    (Dyrecta Lab)

Abstract

This paper is devoted to the analysis of a bilinear optimal control problem subject to the Fokker–Planck equation. The control function depends on time and space and acts as a coefficient of the advection term. For this reason, suitable integrability properties of the control function are required to ensure well posedness of the state equation. Under these low regularity assumptions and for a general class of objective functionals, we prove the existence of optimal controls. Moreover, for common quadratic cost functionals of tracking and terminal type, we derive the system of first-order necessary optimality conditions.

Suggested Citation

  • Arthur Fleig & Roberto Guglielmi, 2017. "Optimal Control of the Fokker–Planck Equation with Space-Dependent Controls," Journal of Optimization Theory and Applications, Springer, vol. 174(2), pages 408-427, August.
    • Handle: RePEc:spr:joptap:v:174:y:2017:i:2:d:10.1007_s10957-017-1120-5
    DOI: 10.1007/s10957-017-1120-5
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    References listed on IDEAS

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    1. Alessio Porretta, 2014. "On the Planning Problem for the Mean Field Games System," Dynamic Games and Applications, Springer, vol. 4(2), pages 231-256, June.
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    Cited by:

    1. Tim Breitenbach & Alfio Borzì, 2020. "The Pontryagin maximum principle for solving Fokker–Planck optimal control problems," Computational Optimization and Applications, Springer, vol. 76(2), pages 499-533, June.

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