Related papers: Controlled Interacting Branching Diffusion Process…
We investigate the long-time evolution of branching diffusion processes (starting with a finite number of particles) in inhomogeneous media. The qualitative behavior of the processes depends on the intensity of the branching. In the…
We extend the convergence analysis for methods solving PDE-constrained optimal control problems containing both discrete and continuous control decisions based on relaxation and rounding strategies to the class of first order semilinear…
In this article, we study the ergodic risk-sensitive control problem for controlled regime-switching diffusions. Under a blanket stability hypothesis, we solve the associated nonlinear eigenvalue problem for weakly coupled systems and…
This papers shows the convergence of optimal control problems where the constraint function is discretised by a particle method. In particular, we investigate the viscous Burgers equation in the whole space $\mathbb R$ by using…
We consider a control problem where the system is driven by a decoupled as well as a coupled forward-backward stochastic differential equation. We prove the existence of an optimal control in the class of relaxed controls, which are…
We introduce the optimality question to the relaxation in multiple control problems described by Sobolev type nonlinear fractional differential equations with nonlocal control conditions in Banach spaces. Moreover, we consider the…
We consider a classical stochastic control problem in which a diffusion process is controlled by a withdrawal process up to a termination time. The objective is to maximize the expected discounted value of the withdrawals until the…
Stochastic optimal control problems with constraints on the probability distribution of the final output are considered. Necessary conditions for optimality in the form of a coupled system of partial differential equations involving a…
Dynamic flux balance analysis of a bioreactor is based on the coupling between a dynamic problem, which models the evolution of biomass, feeding substrates and metabolites, and a linear program, which encodes the metabolic activity inside…
This work collects some methodological insights for numerical solution of a "minimum-dispersion" control problem for nonlinear stochastic differential equations, a particular relaxation of the covariance steering task. The main ingredient…
The optimal controller design problem for a linear, first-order spatially-invariant distributed parameter system is considered. Through a case study of the Linear Quadratic Regulator (LQR) problem for the diffusion equation over the torus,…
We discuss the optimal Markovian coupling before an exponential time of the Kolmogorov diffusion, and a class of related stochastic control problems in which the aim is to hit the origin before an exponential time. We provide a scaling…
In this work, we present numerical analysis for a distributed optimal control problem, with box constraint on the control, governed by a subdiffusion equation which involves a fractional derivative of order $\alpha\in(0,1)$ in time. The…
This paper analyzes a discretization of a stochastic parabolic optimal control problem, where the diffusion term contains the control variable. With rough data, the convergence of the discretization is derived. In addition, a Monte-Carlo…
In this paper we study the existence of sufficiently regular representations of Hamilton-Jacobi equations in the optimal control theory with unbounded control set. We use a new method to construct representations for a wide class of…
We consider the problem of controlling the group behavior of a large number of dynamic systems that are constantly interacting with each other. These systems are assumed to have identical dynamics (e.g., birds flock, robot swarm) and their…
We address the problem of making a managerial decision when the investment project is subsidized, which results in the resolution of an infinite-horizon optimal stopping problem of a switching diffusion driven by either an homogeneous or an…
The smoothing distribution is the conditional distribution of the diffusion process in the space of trajectories given noisy observations made continuously in time. It is generally difficult to sample from this distribution. We use the…
We give a description of cell diffusion in a soft tissue, paying special attention to the coupling of force, matter, and microforce balance laws through a suitable dissipation principle. To this end, we cast our framework into a multi-level…
We consider a controlled-diffusion process pertaining to a chain of distributed systems with random perturbations that satisfies a weak H\"ormander type condition. In particular, we consider a stochastic control problem with the following…