A Fokker-Planck control framework for stochastic systems

DOI10.4171/EMSS/27zbMath1406.93383OpenAlexW2809327218MaRDI QIDQ1755915

Alfio Borzì, Mario Annunziato

Publication date: 11 January 2019

Published in: EMS Surveys in Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4171/emss/27

zbMATH Keywords

Hamilton-Jacobi-Bellman equationhybrid systemsstochastic processprobability density functionFokker-Planck equationsMarkov renewal processesmodel predictive controlscientific computingoptimal control theorynumerical analysismean-field approach

Mathematics Subject Classification ID

Probabilistic models, generic numerical methods in probability and statistics (65C20) Dynamic programming in optimal control and differential games (49L20) Numerical computation of solutions to systems of equations (65H10) Reaction-diffusion equations (35K57) Dynamic programming (90C39) Optimal stochastic control (93E20) Random operators and equations (aspects of stochastic analysis) (60H25) Markov renewal processes, semi-Markov processes (60K15) Existence theories for optimal control problems involving partial differential equations (49J20) Optimality conditions for problems involving randomness (49K45) Hamilton-Jacobi equations (35F21) Numerical methods for variational inequalities and related problems (65K15) Fokker-Planck equations (35Q84)

Related Items

Second-order analysis of Fokker–Planck ensemble optimal control problems ⋮ The Pontryagin maximum principle for solving Fokker-Planck optimal control problems ⋮ Accuracy Estimates for Bilinear Optimal Control Problems Governed by Ordinary Differential Equations ⋮ Controlling a generalized Fokker-Planck equation via inputs with nonlocal action ⋮ Optimal control of electricity input given an uncertain demand ⋮ A Fokker--Planck Approach to the Reconstruction of a Cell Membrane Potential ⋮ Tensor Decomposition Methods for High-dimensional Hamilton--Jacobi--Bellman Equations ⋮ First and second order optimality conditions for the control of Fokker-Planck equations ⋮ Optimal control for stochastic differential equations and related Kolmogorov equations

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