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

Arthur Fleig () and Roberto Guglielmi ()
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Arthur Fleig: University of Bayreuth
Roberto Guglielmi: Dyrecta Lab

Journal of Optimization Theory and Applications, 2017, vol. 174, issue 2, No 4, 408-427

Abstract: 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.

Keywords: Bilinear control; Fokker–Planck equation; Optimal control theory; Optimization in Banach spaces; Probability density function; Stochastic optimal control; 35Q84; 35Q93; 49J20; 49K20 (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s10957-017-1120-5

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