TY  - JOUR
A1  - Breitenbach, Tim
A1  - Borzì, Alfio
T1  - The Pontryagin maximum principle for solving Fokker–Planck optimal control problems
JF  - Computational Optimization and Applications
N2  - The characterization and numerical solution of two non-smooth optimal control problems governed by a Fokker–Planck (FP) equation are investigated in the framework of the Pontryagin maximum principle (PMP). The two FP control problems are related to the problem of determining open- and closed-loop controls for a stochastic process whose probability density function is modelled by the FP equation. In both cases, existence and PMP characterisation of optimal controls are proved, and PMP-based numerical optimization schemes are implemented that solve the PMP optimality conditions to determine the controls sought. Results of experiments are presented that successfully validate the proposed computational framework and allow to compare the two control strategies.
KW  - Fokker–Planck equation
KW  - Pontryagin maximum principle
KW  - non-smooth optimal control problems
KW  - stochastic processes
Y1  - 2020
U6  - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:bvb:20-opus-232665
SN  - 0926-6003
VL  - 76
ER  -