Vortrag im Mathematischen Kolloquium von A. Borzi:
"An Optimal Control Strategy for Probability Density Functions of Stochastic Processes and Piecewise Deterministic Processes"

Vortrag

"An Optimal Control Strategy for Probability Density Functions
of Stochastic Processes and Piecewise Deterministic Processes"

im Mathematischen Kolloquium von

Prof. Dr. Alfio Borzi
Lehrstuhl für Mathematik IX „Wissenschaftliches Rechnen”
Institut für Mathematik
Fakultät für Mathematik und Informatik
Universität Würzburg

am 10. Januar 2013

Abstract:

An efficient framework for the optimal control of probability density functions (PDF) of multidimensional stochastic processes and piecewise deterministic processes is presented. This framework is based on Fokker-Planck-type partial differential equations that govern the time evolution of the PDF of stochastic processes and piecewise deterministic processes. In this approach the control objectives are formulated in terms of the PDF to follow a given trajectory and to reach a desired terminal configuration. The corresponding optimal control problems are formulated as a sequence of open-loop optimality systems in a model predictive control strategy.

We provide a simple derivation of the Fokker-Planck (FP) models: in the case of stochastic (Ito) processes, the FP equation is of parabolic type; in the case of piecewise deterministic processes, the Fokker-Planck model is a first-order hyperbolic system. The proposed control framework is validated with multidimensional biological and financial models, also using Monte Carlo simulation.

Einladung: PDF-file

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