Optimal Control of the Keilson-Storer Master Equation in a Monte Carlo Framework

Bartsch, Jan; Nastasi, Giovanni; Borzì, Alfio

doi:10.1080/23324309.2021.1896552

Cited by 7 publications

(4 citation statements)

References 37 publications

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“…Notice that this structure can also be motivated in the framework of first-and second-moment equations where it appears that u 1 enters in the control of the variance of the process, whereas its mean results controlled by both u 0 and u 1 . We remark that the drift (83) has the form of (7) with n × 2n-matrix with given u min , u max : [0, T ] → R m measurable and bounded such that U T ad ̸ = ∅. We remark that in (84), the time derivative of the control is due to Brockett's concept of minimum attention control aim at penalizing large variation of the control, cf.…”

Section: Extension To Brockett's Ensemble Control Problemsmentioning

confidence: 99%

“…Recently, Brockett's research programme has received much impetus through novel theoretical and numerical work focusing on deterministic models with random initial conditions and the corresponding Liouville equation [5,6], and in the case of a linear Boltzmann equation [7]. The modelling and simulation of FP ensemble optimal control problems has been investigated in view of their large applicability [12,[33][34][35].…”

Section: Introductionmentioning

confidence: 99%

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Second-order analysis of Fokker–Planck ensemble optimal control problems

Körner¹,

Borzì²

2022

ESAIM: COCV

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Ensemble optimal control problems governed by a Fokker–Planck equation with space–time dependent controls are investigated. These problems require the minimisation of objective functionals of probability type and aim at determining robust control mechanisms for the ensemble of trajectories of the stochastic system defining the Fokker–Planck model. In this work, existence of optimal controls is proved and a detailed analysis of their characterization by first– and second–order optimality conditions is presented. For this purpose, the well–posedness of the Fokker–Planck equation, and new estimates concerning an inhomogeneous Fokker–Planck model are discussed, which are essential to prove the necessary regularity and compactness of the control–to–state map appearing in the first–and second–order analysis.

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Section: Extension To Brockett's Ensemble Control Problemsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Second-order analysis of Fokker–Planck ensemble optimal control problems

Körner¹,

Borzì²

2022

ESAIM: COCV

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“…We remark that, in both cases, these control fields can be determined as solutions to kinetic optimal control problems with ensemble cost functionals. In the realm of optimal control theory, these functionals have been proposed and studied in [10,11,12] and later in [3,4]. However, they have been well-known in stochastics and statistical mechanics for a long time as expected value functionals.…”

mentioning

confidence: 99%

“…We would like to point out that the investigation of open-loop optimal control problems governed by kinetic models with collision is an emerging topic with only few contributions [1,2,4,13,25,32]. This is particularly true for works concerning the solution of these problems in the framework of Monte Carlo methods.…”

mentioning

confidence: 99%

On the stabilization of a kinetic model by feedback-like control fields in a Monte Carlo framework

Bartsch,

Borzì

2024

KRM

Self Cite

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The construction of feedback-like control fields for a kinetic model in phase space is investigated. The purpose of these controls is to drive an initial density of particles in the phase space to reach a desired cyclic trajectory and follow it in a stable way. For this purpose, an ensemble optimal control problem governed by the kinetic model is formulated in a way that is amenable to a Monte Carlo approach. The proposed formulation allows to define a oneshot solution procedure consisting in a backward solve of an augmented adjoint kinetic model. Results of numerical experiments demonstrate the effectiveness of the proposed control strategy.

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Adjoint-Based Calibration of Nonlinear Stochastic Differential Equations

Bartsch,

Denk,

Volkwein

2024

Appl Math Optim

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To study the nonlinear properties of complex natural phenomena, the evolution of the quantity of interest can be often represented by systems of coupled nonlinear stochastic differential equations (SDEs). These SDEs typically contain several parameters which have to be chosen carefully to match the experimental data and to validate the effectiveness of the model. In the present paper the calibration of these parameters is described by nonlinear SDE-constrained optimization problems. In the optimize-before-discretize setting a rigorous analysis is carried out to ensure the existence of optimal solutions and to derive necessary first-order optimality conditions. For the numerical solution a Monte–Carlo method is applied using parallelization strategies to compensate for the high computational time. In the numerical examples an Ornstein–Uhlenbeck and a stochastic Prandtl–Tomlinson bath model are considered.

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Optimal Control of the Keilson-Storer Master Equation in a Monte Carlo Framework

Cited by 7 publications

References 37 publications

Second-order analysis of Fokker–Planck ensemble optimal control problems

Second-order analysis of Fokker–Planck ensemble optimal control problems

On the stabilization of a kinetic model by feedback-like control fields in a Monte Carlo framework

Adjoint-Based Calibration of Nonlinear Stochastic Differential Equations

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