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This work deals with the exponential stabilization of a system of three semilinear parabolic partial differential equations (PDEs), written in a strict feedforward form. The diffusion coefficients are considered distinct and the PDEs are…
In this paper, we establish some second order necessary/sufficient optimality conditions for optimal control problems of stochastic evolution equations in infinite dimensions. The control acts on both the drift and diffusion terms and the…
We discuss several optimization procedures to solve finite element approximations of linear-quadratic Dirichlet optimal control problems governed by an elliptic partial differential equation posed on a 2D or 3D Lipschitz domain. The control…
State-dependent parameter identification, where unknown model parameters depend on one or more state variables in partial differential equations (PDEs) or coupled PDE systems, is fundamental to a wide range of problems in physics,…
Many physical phenomena, governed by partial differential equations (PDEs), are second order in nature. This makes sense to pose the control on the second order derivatives of the field solution, in addition to zero and first order ones, to…
We consider both discrete and continuous control problems constrained by a fixed budget of some resource, which may be renewed upon entering a preferred subset of the state space. In the discrete case, we consider both deterministic and…
We study sparse solutions of optimal control problems governed by PDEs with uncertain coefficients. We propose two formulations, one where the solution is a deterministic control optimizing the mean objective, and a formulation aiming at…
We consider the optimal control problem of stochastic evolution equations in a Hilbert space under a recursive utility, which is described as the solution of a backward stochastic differential equation (BSDE). A very general maximum…
This work discusses the finite element discretization of an optimal control problem for the linear wave equation with time-dependent controls of bounded variation. The main focus lies on the convergence analysis of the discretization…
We introduce a semidefinite relaxation for optimal control of linear systems with time scaling. These problems are inherently nonconvex, since the system dynamics involves bilinear products between the discretization time step and the…
This paper addresses the problem of solving a class of nonlinear optimal control problems (OCP) with infinite-dimensional linear state constraints involving Riesz-spectral operators. Each instance within this class has time/control…
This paper provides global exponential stabilization results by means of boundary feedback control for 1-D nonlinear unstable reaction-diffusion Partial Differential Equations (PDEs) with nonlinearities of superlinear growth. The class of…
We consider a bilinear optimal control problem with pointwise tracking for a semilinear elliptic PDE in two and three dimensions. The control variable enters the PDE as a (reaction) coefficient and the cost functional contains point…
An optimal control problem associated to the Keller-Segel with logistic reaction system will be studied in $2D$ domains. The control acts in a bilinear form only in the chemical equation. The existence of optimal control and a necessary…
This work investigates an elliptic optimal control problem defined on uncertain domains and discretized by a fictitious domain finite element method and cut elements. Key ingredients of the study are to manage cases considering the usually…
We consider an optimal control problem on a bounded domain $\Omega\subset\mathbb{R}^2,$ governed by a parabolic convection--diffusion--reaction equation with pointwise control constraints. We follow the optimize--then--discretize approach,…
Recent years have seen the emergence of nonlinear methods for solving partial differential equations (PDEs), such as physics-informed neural networks (PINNs). While these approaches often perform well in practice, their theoretical analysis…
We derive existence results and first order necessary optimality conditions for optimal control problems governed by quasilinear parabolic PDEs with a class of first order nonlinearities that include for instance quadratic gradient terms.…
This paper investigates a class of controlled stochastic partial differential equations (SPDEs) arising in the modeling of composite materials with spatially varying properties. The state equation describes the evolution of a material…
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…