On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks

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Applied Mathematics

ISSN Print: 2152-7385
ISSN Online: 2152-7393
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"On the Connection between the Hamilton-Jacobi-Bellman and the Fokker-Planck Control Frameworks"
written by Mario Annunziato, Alfio Borzì, Fabio Nobile, Raul Tempone,
published by Applied Mathematics, Vol.5 No.16, 2014

has been cited by the following article(s):

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[10]	Multilevel techniques for the solution of HJB minimum-time control problems
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[13]	The Fokker–Planck Framework in the Modeling of Pedestrians' Motion
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[15]	Entropic Dynamics in Neural Networks, the Renormalization Group and the Hamilton-Jacobi-Bellman Equation
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[16]	Two-level method for a time-independent Fokker-Planck control problem
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[17]	Towards a solution of mean-field control problems using model predictive control
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[18]	A Fokker–Planck control framework for stochastic systems
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[19]	Open and closed-loop stochastic dynamics of a class of nonlinear chemical processes with multiplicative noise
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[20]	Global-nonlinear stochastic dynamics of a class of two-state two-parameter non-isothermal continuous stirred tank reactors
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[21]	Optimal Design for Estimation in Diffusion Processes from First Hitting Times
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[25]	Estimates on the minimal stabilizing horizon length in Model Predictive Control for the Fokker-Planck equation
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[31]	Stochastic control with state constraints of a photovoltaic plant with batteries.

[1]	An optimal control problem for the continuity equation arising in smart charging Journal of Mathematical Analysis and Applications, 2024 DOI:10.1016/j.jmaa.2023.127891

[2]	Stochastic control with state constraints via the Fokker–Planck equation. Application to renewable energy plants with batteries Comptes Rendus. Mécanique, 2024 DOI:10.5802/crmeca.236

[3]	Stochastic control with state constraints via the Fokker–Planck equation. Application to renewable energy plants with batteries Comptes Rendus. Mécanique, 2024 DOI:10.5802/crmeca.236

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[5]	An optimal control problem for the continuity equation arising in smart charging Journal of Mathematical Analysis and Applications, 2024 DOI:10.1016/j.jmaa.2023.127891

[6]	Optimal Control of Diffusion Processes: Infinite-Order Variational Analysis and Numerical Solution IEEE Control Systems Letters, 2024 DOI:10.1109/LCSYS.2024.3410632

[7]	On the closed-loop stochastic dynamics of two-state nonlinear exothermic CSTRs with PI temperature control Computers & Chemical Engineering, 2023 DOI:10.1016/j.compchemeng.2023.108246

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[9]	On the closed-loop stochastic dynamics of two-state nonlinear exothermic CSTRs with PI temperature control Computers & Chemical Engineering, 2023 DOI:10.1016/j.compchemeng.2023.108246

[10]	On the closed-loop stochastic dynamics of two-state nonlinear exothermic CSTRs with PI temperature control Computers & Chemical Engineering, 2023 DOI:10.1016/j.compchemeng.2023.108246

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[12]	Numerical solution to 3D bilinear Fokker–Planck control problem International Journal of Computer Mathematics, 2022 DOI:10.1080/00207160.2022.2067987

[13]	Probabilistic design of optimal sequential decision-making algorithms in learning and control Annual Reviews in Control, 2022 DOI:10.1016/j.arcontrol.2022.09.003

[14]	Multilevel Techniques for the Solution of HJB Minimum-Time Control Problems Journal of Systems Science and Complexity, 2021 DOI:10.1007/s11424-021-0253-7

[15]	Characterization with Fokker–Planck theory of the nonlinear stochastic dynamics of a class of two-state continuous bioreactors Journal of Process Control, 2021 DOI:10.1016/j.jprocont.2021.04.004

[16]	Multilevel Techniques for the Solution of HJB Minimum-Time Control Problems Journal of Systems Science and Complexity, 2021 DOI:10.1007/s11424-021-0253-7

[17]	Characterization with Fokker–Planck theory of the nonlinear stochastic dynamics of a class of two-state continuous bioreactors Journal of Process Control, 2021 DOI:10.1016/j.jprocont.2021.04.004

[18]	Two-level method for a time-independent Fokker–Planck control problem International Journal of Computer Mathematics, 2021 DOI:10.1080/00207160.2020.1825696

[19]	Towards a solution of mean-field control problems using model predictive control IFAC-PapersOnLine, 2020 DOI:10.1016/j.ifacol.2020.12.1086

[20]	The Pontryagin maximum principle for solving Fokker–Planck optimal control problems Computational Optimization and Applications, 2020 DOI:10.1007/s10589-020-00187-x

[21]	Entropic Dynamics in Neural Networks, the Renormalization Group and the Hamilton-Jacobi-Bellman Equation Entropy, 2020 DOI:10.3390/e22050587

[22]	Crowd Dynamics, Volume 2 Modeling and Simulation in Science, Engineering and Technology, 2020 DOI:10.1007/978-3-030-50450-2_6

[23]	Towards a solution of mean-field control problems using model predictive control IFAC-PapersOnLine, 2020 DOI:10.1016/j.ifacol.2020.12.1086

[24]	Towards a solution of mean-field control problems using model predictive control IFAC-PapersOnLine, 2020 DOI:10.1016/j.ifacol.2020.12.1086

[25]	Entropic Dynamics in Neural Networks, the Renormalization Group and the Hamilton-Jacobi-Bellman Equation Entropy, 2020 DOI:10.3390/e22050587

[26]	Open and closed-loop stochastic dynamics of a class of nonlinear chemical processes with multiplicative noise Journal of Process Control, 2018 DOI:10.1016/j.jprocont.2018.03.004

[27]	CALIBRATION OF LÉVY PROCESSES USING OPTIMAL CONTROL OF KOLMOGOROV EQUATIONS WITH PERIODIC BOUNDARY CONDITIONS Mathematical Modelling and Analysis, 2018 DOI:10.3846/mma.2018.024

[28]	Global-nonlinear stochastic dynamics of a class of two-state two-parameter non-isothermal continuous stirred tank reactors Journal of Process Control, 2018 DOI:10.1016/j.jprocont.2018.07.012

[29]	Optimal Design for Estimation in Diffusion Processes from First Hitting Times SIAM/ASA Journal on Uncertainty Quantification, 2017 DOI:10.1137/16M1060376

[30]	A Fokker–Planck approach to control collective motion Computational Optimization and Applications, 2017 DOI:10.1007/s10589-017-9944-3

[31]	State Constrained Optimal Control via the Fokker-Planck Equation IFAC-PapersOnLine, 2017 DOI:10.1016/j.ifacol.2017.08.893

[32]	State Constrained Optimal Control via the Fokker-Planck Equation IFAC-PapersOnLine, 2017 DOI:10.1016/j.ifacol.2017.08.893

[33]	Dynamic Programming for Mean-Field Type Control Journal of Optimization Theory and Applications, 2016 DOI:10.1007/s10957-015-0785-x

[34]	Stochastic modelling and control of antibiotic subtilin production Journal of Mathematical Biology, 2016 DOI:10.1007/s00285-016-0968-6

[35]	Closed Loop Neuroscience 2016 DOI:10.1016/B978-0-12-802452-2.00008-1

[36]	Estimates on the Minimal Stabilizing Horizon Length in Model Predictive Control for the Fokker-Planck Equation*This work was supported by the DFG project Model Predictive Control for the Fokker-Planck Equation, GR 1569/15-1. The paper was written while the second author was visiting the University of Newcastle, Australia. IFAC-PapersOnLine*, 2016 DOI:10.1016/j.ifacol.2016.07.451

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