A Fokker-Planck control framework for stochastic systems
type: Item
instance of: scholarly article
title: A Fokker-Planck control framework for stochastic systems
zbMATH Open document ID: 1406.93383
DOI: 10.4171/EMSS/27
published in: EMS Surveys in Mathematical Sciences
publication date: 2019-01-11T00:00:00Z
review text: Summary: A new framework for the optimal control of Probability Density Functions (PDF) of stochastic processes is reviewed. This framework is based on Fokker-Planck (FP) partial differential equations that govern the time evolution of the PDF of stochastic systems and on control objectives that may require to follow a given PDF trajectory or to minimize an expectation functional.{ }Corresponding to different stochastic processes, different FP equations are obtained. In particular, FP equations of parabolic, fractional parabolic, integro parabolic, and hyperbolic type are discussed. The corresponding optimization problems are deterministic and can be formulated in an open-loop framework and within a closed-loop model predictive control strategy. The connection between the dynamic programming scheme given by the Hamilton-Jacobi-Bellman equation and the FP control framework is discussed. Under appropriate assumptions, it is shown that the two strategies are equivalent. Some applications of the FP control framework to different models are discussed and its extension in a mean-field framework is elucidated.
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 60K15
Mathematics Subject Classification ID: 49K45
Mathematics Subject Classification ID: 35F21
Mathematics Subject Classification ID: 35K57
Mathematics Subject Classification ID: 35Q84
Mathematics Subject Classification ID: 49J20
Mathematics Subject Classification ID: 49L20
Mathematics Subject Classification ID: 65C20
Mathematics Subject Classification ID: 65H10
Mathematics Subject Classification ID: 60H25
Mathematics Subject Classification ID: 65K15
Mathematics Subject Classification ID: 90C39
zbMATH DE Number: 7000372
zbMATH Keywords: Fokker-Planck equations
zbMATH Keywords: Hamilton-Jacobi-Bellman equation
zbMATH Keywords: stochastic process
zbMATH Keywords: hybrid systems
zbMATH Keywords: Markov renewal processes
zbMATH Keywords: probability density function
zbMATH Keywords: mean-field approach
zbMATH Keywords: optimal control theory
zbMATH Keywords: model predictive control
zbMATH Keywords: numerical analysis
zbMATH Keywords: scientific computing
author: M. Annunziato
author: Alfio Borzì
MaRDI profile type: Publication
cites work: Existence and uniqueness of optimal control for a distributed-parameter bilinear system
cites work: Theory of hybrid dynamical systems and its applications to biological and medical systems
cites work: Analysis Of Upwind Method For Piecewise Deterministic Markov Processes
cites work: OPTIMAL CONTROL OF PROBABILITY DENSITY FUNCTIONS OF STOCHASTIC PROCESSES
cites work: A Fokker-Planck control framework for multidimensional stochastic processes
cites work: Fokker-Planck-based control of a two-level open quantum system
cites work: Optimal control of a class of piecewise deterministic processes
cites work: A fractional Fokker-Planck control framework for subdiffusion processes
cites work: CALIBRATION OF LÉVY PROCESSES USING OPTIMAL CONTROL OF KOLMOGOROV EQUATIONS WITH PERIODIC BOUNDARY CONDITIONS
cites work: Lévy Processes and Stochastic Calculus
cites work: Q5573634
cites work: Quantum trajectories and measurements in continuous time. The diffusive case
cites work: MDP algorithms for portfolio optimization problems in pure jump markets
cites work: Estimation of Variable Cefficients in the Fokker–Planck Quations Using Moving Node Finite Elements
cites work: The Pontryagin Maximum Principle From Dynamic Programming and Viscosity Solutions to First-Order Partial Differential Equations
cites work: A unifying formulation of the Fokker-Planck-Kolmogorov equation for general stochastic hybrid systems
cites work: Mean Field Games and Mean Field Type Control Theory
cites work: Optimal policies for controlled Markov chains with a constraint
cites work: Fokker–Planck–Kolmogorov Equations
cites work: Distances between transition probabilities of diffusions and applications to nonlinear Fokker-Planck-Kolmogorov equations
cites work: Computational Optimization of Systems Governed by Partial Differential Equations
cites work: A stochastic particle method for the McKean-Vlasov and the Burgers equation
cites work: Q2762108
cites work: Q3596129
cites work: A Conservative and Entropy Scheme for a Simplified Model of Granular Media
cites work: On the Chang and Cooper scheme applied to a linear Fokker-Planck equation
cites work: Second order optimality conditions and their role in PDE control
cites work: Stochastic Hybrid Systems
cites work: A practical difference scheme for Fokker-Planck equations
cites work: Piecewise deterministic Markov processes applied to fatigue crack growth modelling
cites work: Subtilin Production byBacillus Subtilis: Stochastic Hybrid Models and Parameter Identification
cites work: The Relationship between the Maximum Principle and Dynamic Programming
cites work: A finite-volume scheme for dynamic reliability models
cites work: Characterization of the marginal distributions of Markov processes used in dynamic reliability
cites work: Average Continuous Control of Piecewise Deterministic Markov Processes
cites work: User’s guide to viscosity solutions of second order partial differential equations
cites work: Q4169795
cites work: Q3680030
cites work: Fast Solution of Parabolic Problems in the Tensor Train/Quantized Tensor Train Format with Initial Application to the Fokker--Planck Equation
cites work: On parameter identification in stochastic differential equations by penalized maximum likelihood
cites work: Q5359695
cites work: Tikhonov regularization applied to the inverse problem of option pricing: convergence analysis and rates
cites work: An implicit finite volume scheme for a scalar hyperbolic problem with measure data related to piecewise deterministic Markov processes
cites work: Non-equilibrium thermodynamics of piecewise deterministic Markov processes

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Optimal control of the Fokker-Planck equation with space-dependent controls

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Controlled Markov processes and viscosity solutions

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Q4086303

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Q5447271

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Analysis of splitting methods for solving a partial integro-differential Fokker-Planck equation

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Q5653395

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: The quantum-state diffusion model applied to open systems

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Approximation properties of receding horizon optimal control

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Nonlinear model predictive control. Theory and algorithms.

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: On the Infinite Horizon Performance of Receding Horizon Controllers

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: An Implementation Framework for Solving High-Dimensional PDEs on Massively Parallel Computers

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Balanced averaging of bilinear systems with applications to stochastic control

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: An algorithmic introduction to numerical simulation of stochastic differential equations

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Hybrid Systems: Computation and Control

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Fokker-Planck and Fortet equation-based parameter estimation for a leaky integrate-and-fire model with sinusoidal and stochastic forcing

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Optimal Design for Estimation in Diffusion Processes from First Hitting Times

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Receding horizon optimal control for infinite dimensional systems

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Parameter estimation for forward Kolmogorov equation with application to nonlinear exchange rate dynamics

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Tracking control of non-linear stochastic systems by using path cross-entropy and Fokker-Planck equation

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: A stochastic model related to the telegrapher's equation

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: More is the same; phase transitions and mean field theories

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Towards fully probabilistic control design

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: COMPUTATION OF MEAN FIELD EQUILIBRIA IN ECONOMICS

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Mean field games

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Existence and Uniqueness of Solutions to Fokker–Planck Type Equations with Irregular Coefficients

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Q5601627

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: On the Hamilton-Jacobi-Bellman equations

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Fractional Langevin equation with α-stable noise. A link to fractional ARIMA time series

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: The random walk's guide to anomalous diffusion: A fractional dynamics approach

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Analysis of the Chang-Cooper discretization scheme for a class of Fokker-Planck equations

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: A HERMITE SPECTRAL METHOD FOR A FOKKER-PLANCK OPTIMAL CONTROL PROBLEM IN AN UNBOUNDED DOMAIN

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: First and second-order necessary and sufficient optimality conditions for infinite-dimensional programming problems

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Receding horizon control of nonlinear systems

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Q1019056

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Q5671442

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Applied stochastic control of jump diffusions

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: On filtered binary processes

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Stochastic Methods and Their Applications to Communications

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Existence of optimal controls for systems governed by parabolic partial differential equations with Cauchy boundary conditions

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: The Fokker-Planck equation. Methods of solution and applications.

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: A Fokker–Planck Feedback Control-Constrained Approach for Modelling Crowd Motion

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: A Fokker-Planck approach to control collective motion

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Theory and applications of stochastic processes. An analytical approach

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Existence and Uniqueness of Optimal Controls for a Quasilinear Parabolic Equation

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Existence and uniqueness of viscosity solutions for QVI associated with impulse control of jump-diffusions

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Q4223074

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Q3358031

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Stochastic modelling and control of antibiotic subtilin production

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Q3558349

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Stochastic Approaches for Systems Biology

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Robust control of the output probability density functions for multivariable stochastic systems with guaranteed stability

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Ergodic properties of anomalous diffusion processes

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: A Genuinely High Order Total Variation Diminishing Scheme for One-Dimensional Scalar Conservation Laws

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Robust tracking controller design for non-Gaussian singular uncertainty stochastic distribution systems

A Fokker-Planck control framework for stochastic systems (cites work)
cites work: Multigrid for High-Dimensional Elliptic Partial Differential Equations on Non-equidistant Grids

A Fokker-Planck control framework for stochastic systems (full work available at URL)
full work available at URL: https://doi.org/10.4171/emss/27

A Fokker-Planck control framework for stochastic systems (OpenAlex ID)
OpenAlex ID: W2809327218