Related papers: Homogenization Results for a Deterministic Multi-d…
We study a homogenisation problem for problems of mixed type in the framework of evolutionary equations. The change of type is highly oscillatory. The numerical treatment is done by a discontinuous Galerkin method in time and a continuous…
This article is a continuation of a previous work where we studied infinite horizon control problems for which the dynamic, running cost and control space may be different in two half-spaces of some euclidian space $\R^N$. In this article…
The recent approach based on Hamiltonian systems and the implicit parametri\-za\-tion theorem, provides a general fixed domain approximation method in shape optimization problems, using optimal control theory. In previous works, we have…
The purpose of this paper is to address a class of hybrid optimal control problems constrained with hyperelasticity and constant global volume. This type of problems can intervene for example in the mechanical aspects of cardiac activity.…
We perform a detailed study of a simple mathematical model addressing the problem of optimally regulating a process subject to periodic external forcing, which is interesting both in view of its direct applications and as a prototype for…
This paper presents the design and analysis of a Hybrid High-Order (HHO) approximation for a distributed optimal control problem governed by the Poisson equation. We propose three distinct schemes to address unconstrained control problems…
We study a stochastic control problem for continuous multidimensional martingales with fixed quadratic variation. In a radially symmetric environment, we are able to find an explicit solution to the control problem and find an optimal…
In this manuscript, we study optimal control problems for stochastic delay differential equations using the dynamic programming approach in Hilbert spaces via viscosity solutions of the associated Hamilton-Jacobi-Bellman equations. We show…
We discuss the multilevel control problem for linear dynamical systems, consisting in designing a piece-wise constant control function taking values in a finite-dimensional set. In particular, we provide a complete characterization of…
We present a Hilbert space perspective to homogenization of standard linear evolutionary boundary value problems in mathematical physics and provide a unified treatment for (non-)periodic homogenization problems in thermodynamics,…
Initially introduced in the framework of quantum control, the so-called "monotonic algorithms" have demonstrated excellent numerical performance when dealing with bilinear optimal control problems. This paper presents a unified formulation…
This article concerns a class of time-optimal state constrained control problems with dynamics defined by an ordinary differential equation involving a three-dimensional steady flow vector field. The problem is solved via an indirect method…
In this paper we study optimal control problems in Wasserstein spaces, which are suitable to describe macroscopic dynamics of multi-particle systems. The dynamics is described by a parametrized continuity equation, in which the Eulerian…
In this paper, a quadratic optimal control problem is considered for second-order parabolic PDEs with homogeneous Dirichlet boundary conditions, in which the "point" control function (depending only on time) constitutes a source term. These…
We consider a Hamilton-Jacobi equation where the Hamiltonian is periodic in space and coercive and convex in momentum. Combining the representation formula from optimal control theory and a theorem of Alexander, originally proved in the…
Optimal control problem is typically solved by first finding the value function through Hamilton-Jacobi equation (HJE) and then taking the minimizer of the Hamiltonian to obtain the control. In this work, instead of focusing on the value…
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…
The present paper is concerned with a space-time homogenization problem for nonlinear diffusion equations with periodically oscillating (in space and time) coefficients. Main results consist of a homogenization theorem (i.e., convergence of…
Motivated by the applications, a class of optimal control problems is investigated, where the goal is to influence the behavior of a given population through another controlled one interacting with the first. Diffusive terms accounting for…
A Deterministic affine quadratic optimal control problem is considered. Due to the nature of the problem, optimal controls exist under some very mild conditions. Further, it is shown that under some assumptions, the value function is…