Dan Goreac
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View article: Generating functions for irreversible Hamiltonian systems
Generating functions for irreversible Hamiltonian systems Open
View article: About the Bang-Bang Principle for Controlled Affine Dynamics With Brownian Noise
About the Bang-Bang Principle for Controlled Affine Dynamics With Brownian Noise Open
We revisit the Bang-Bang Principle, established for deterministic affine controlled dynamics, in a stochastic framework when the dynamics is subject to a Brownian motion. We show that such a Principle does not hold in general in this setti…
View article: Optimal control under action duration constraint for non-convex dynamics
Optimal control under action duration constraint for non-convex dynamics Open
International audience
View article: Further results about L ∞ /L 1 duality and applications to the SIR epidemiological model
Further results about L ∞ /L 1 duality and applications to the SIR epidemiological model Open
International audience
View article: Optimality of vaccination for an SIR epidemic with an ICU constraint
Optimality of vaccination for an SIR epidemic with an ICU constraint Open
This paper studies an optimal control problem for a class of SIR epidemic models, in scenarios in which the infected population is constrained to be lower than a critical threshold imposed by the ICU (intensive care unit) capacity. The vac…
View article: Stochastic porous media equation with Robin boundary conditions, gravity-driven infiltration and multiplicative noise
Stochastic porous media equation with Robin boundary conditions, gravity-driven infiltration and multiplicative noise Open
We aim at studying a novel mathematical model associated to a physical phenomenon of infiltration in an homogeneous porous medium. The particularities of our system are connected to the presence of a gravitational acceleration term proport…
View article: $\mathbb {L^\infty }$/$\mathbb {L}^{1}$ Duality Results in Optimal Control Problems
$\mathbb {L^\infty }$/$\mathbb {L}^{1}$ Duality Results in Optimal Control Problems Open
International audience
View article: Generating functions for irreversible Hamiltonian systems
Generating functions for irreversible Hamiltonian systems Open
The definition of conservative-irreversible functions is extended to smooth manifolds. The local representation of these functions is studied and reveals that not each conservative-irreversible function is given by the weighted product of …
View article: About optimal control problem under action duration constraint and infimum-gap
About optimal control problem under action duration constraint and infimum-gap Open
International audience
View article: Improved regularity for the stochastic fast diffusion equation
Improved regularity for the stochastic fast diffusion equation Open
We prove that the solution to the singular-degenerate stochastic fast-diffusion equation with parameter $m\in (0,1)$, with zero Dirichlet boundary conditions on a bounded domain in any spatial dimension, and driven by linear multiplicative…
View article: Improved regularity for the stochastic fast diffusion equation
Improved regularity for the stochastic fast diffusion equation Open
We prove that the solution to the singular-degenerate stochastic fast-diffusion equation with parameter $m\in (0,1)$, with zero Dirichlet boundary conditions on a bounded domain in any spatial dimension, and driven by linear multiplicative…
View article: A Stochastic Porous Media Schr{ö}dinger Equation: Feynman-type Motivation, Well-Posedness and Control Interpretation
A Stochastic Porous Media Schr{ö}dinger Equation: Feynman-type Motivation, Well-Posedness and Control Interpretation Open
This paper's aim is threefold. First, using Feynman's path approach to the derivation of theclassical Schr{ö}dinger's equation in [6] and by introducing a slight path (or wave) dependency ofthe action, we derive a new class of equations of…
View article: Explicit mathematical epidemiology results on age renewal kernels and R0 formulas are often consequences of the rank one property of the next generation matrix
Explicit mathematical epidemiology results on age renewal kernels and R0 formulas are often consequences of the rank one property of the next generation matrix Open
A very large class of ODE epidemic models (2.2) discussed in this paper enjoys the property of admitting also an integral renewal formulation, with respect to an "age of infection kernel" a(t) which has a matrix exponential form (3.2). We …
View article: Infinite horizon optimal control of a SIR epidemic under an ICU constraint
Infinite horizon optimal control of a SIR epidemic under an ICU constraint Open
The aim of this paper is to provide a rigorous mathematical analysis of an optimal control problem of a SIR epidemic on an infinite horizon. A state constraint related to intensive care units (ICU) capacity is imposed and the objective fun…
View article: L$\infty$/L1 Duality Results In Optimal Control Problems
L$\infty$/L1 Duality Results In Optimal Control Problems Open
We provide a duality result linking the value function for a control problem with supremum cost H under an isoperimetric inequality G $\le$ gmax, and the value function for the same controlled dynamics with cost G and state constraint H $\…
View article: L∞/L1 Duality Results In Optimal Control Problems
L∞/L1 Duality Results In Optimal Control Problems Open
View article: The stochastic fast logarithmic equation in $\mathbb{R}^{d}$ with multiplicative Stratonovich noise
The stochastic fast logarithmic equation in $\mathbb{R}^{d}$ with multiplicative Stratonovich noise Open
This paper is concerned with the existence and uniqueness of the solution for the stochastic fast logarithmic equation with Stratonovich multiplicative noise in $\mathbb{R}^{d}$ for $d\geqslant 3$. It provides an answer to a critical case …
View article: An Age of Infection Kernel, an R Formula, and Further Results for Arino–Brauer A, B Matrix Epidemic Models with Varying Populations, Waning Immunity, and Disease and Vaccination Fatalities
An Age of Infection Kernel, an R Formula, and Further Results for Arino–Brauer A, B Matrix Epidemic Models with Varying Populations, Waning Immunity, and Disease and Vaccination Fatalities Open
In this work, we first introduce a class of deterministic epidemic models with varying populations inspired by Arino et al. (2007), the parameterization of two matrices, demography, the waning of immunity, and vaccination parameters. Simil…
View article: On the near-viability property of controlled mean-field flows
On the near-viability property of controlled mean-field flows Open
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View article: On the Design Techniques for Safety Zones In Brownian-Driven Epidemic Models
On the Design Techniques for Safety Zones In Brownian-Driven Epidemic Models Open
This paper is concerned with the mathematical description of safety (herd immunity and feasible) zones for non-pharmaceutically controlled Brownian-driven compartmental models when intensive care units (ICU) restriction are enforced. The c…
View article: The Stochastic Fast Logarithmic Equation In Rd With Multiplicative Stratonovich Noise
The Stochastic Fast Logarithmic Equation In Rd With Multiplicative Stratonovich Noise Open
View article: SIR Epidemics with State-Dependent Costs and ICU Constraints: A Hamilton–Jacobi Verification Argument and Dual LP Algorithms
SIR Epidemics with State-Dependent Costs and ICU Constraints: A Hamilton–Jacobi Verification Argument and Dual LP Algorithms Open
View article: Linearisation Techniques and the Dual Algorithm for a Class of Mixed Singular/Continuous Control Problems in Reinsurance. Part I: Theoretical Aspects
Linearisation Techniques and the Dual Algorithm for a Class of Mixed Singular/Continuous Control Problems in Reinsurance. Part I: Theoretical Aspects Open
View article: Optimizing Dividends and Capital Injections Limited by Bankruptcy, and Practical Approximations for the Cramér-Lundberg Process
Optimizing Dividends and Capital Injections Limited by Bankruptcy, and Practical Approximations for the Cramér-Lundberg Process Open
View article: Asymptotic issue for porous media systems with linear multiplicative gradient-type noise via state constrained arguments
Asymptotic issue for porous media systems with linear multiplicative gradient-type noise via state constrained arguments Open
The aim of the present paper is to provide necessary and sufficient conditions to maintain a stochastic coupled system, with porous media components and gradient-type noise in a prescribed set of constraints by using internal controls. Thi…
View article: State-constrained porous media control systems with application to stabilization
State-constrained porous media control systems with application to stabilization Open
We aim at providing a characterization of the ability to maintain a stochastic coupled system with porous media components in a prescribed set of constraints by using internal controls. This property is proven via a quasi-tangency local-in…
View article: On matrix-SIR Arino models with linear birth rate, loss of immunity, disease and vaccination fatalities, and their approximations
On matrix-SIR Arino models with linear birth rate, loss of immunity, disease and vaccination fatalities, and their approximations Open
In this work we study the stability properties of the equilibrium points of deterministic epidemic models with nonconstant population size. Models with nonconstant population have been studied in the past only in particular cases, two of w…
View article: On matrix-SIR Arino models with linear birth rate, loss of immunity,\n disease and vaccination fatalities, and their approximations
On matrix-SIR Arino models with linear birth rate, loss of immunity,\n disease and vaccination fatalities, and their approximations Open
In this work we study the stability properties of the equilibrium points of\ndeterministic epidemic models with nonconstant population size. Models with\nnonconstant population have been studied in the past only in particular cases,\ntwo o…
View article: Optimal control of a SIR epidemic with ICU constraints and target objectives
Optimal control of a SIR epidemic with ICU constraints and target objectives Open
View article: SIR Epidemics With State-Dependent Costs and ICU Constraints: A Hamilton-Jacobi Verification Argument and Dual LP Algorithms
SIR Epidemics With State-Dependent Costs and ICU Constraints: A Hamilton-Jacobi Verification Argument and Dual LP Algorithms Open
The aim of this paper is twofold. On one hand, we strive to give a simpler proof of the optimality of greedy controls when the cost of interventions is control-affine and the dynamics follow a state-constrained controlled SIR model. This i…