Related papers: Mixed virtual element methods for elliptic optimal…
Though switched dynamical systems have shown great utility in modeling a variety of physical phenomena, the construction of an optimal control of such systems has proven difficult since it demands some type of optimal mode scheduling. In…
We focus on elliptic quasi-variational inequalities (QVIs) of obstacle type and prove a number of results on the existence of solutions, directional differentiability and optimal control of such QVIs. We give three existence theorems based…
A time optimal attitude control problem is studied for the dynamics of a rigid body. The objective is to minimize the time to rotate the rigid body to a desired attitude and angular velocity while subject to constraints on the control…
We consider the finite element discretization and the iterative solution of singularly perturbed elliptic reaction-diffusion equations in three-dimensional computational domains. These equations arise from the optimality conditions for…
The aim of the present work is to derive a error estimates for the Laplace eigenvalue problem in mixed form, by means of a virtual element method. With the aid of the theory for non-compact operators, we prove that the proposed method is…
Hybrid quantum-classical algorithms hold great promise for solving quantum control problems on near-term quantum computers. In this work, we employ the hybrid framework that integrates digital quantum simulation with classical optimization…
This manuscript presents a framework for using multilevel quadrature formulae to compute the solution of optimal control problems constrained by random partial differential equations. Our approach consists in solving a sequence of optimal…
This paper presents a rigorous finite element framework for solving an optimal control problem governed by the steady Navier-Stokes-Brinkman equations, focusing on identifying a scalar permeability parameter $\gamma$ from local velocity…
An effective form of the Variation Evolving Method (VEM), which originates from the continuous-time dynamics stability theory, is developed for the classic time-optimal control problem with control constraint. Within the mathematic…
We consider the integral definition of the fractional Laplacian and analyze a linear-quadratic optimal control problem for the so-called fractional heat equation; control constraints are also considered. We derive existence and uniqueness…
In this work, we use the integral definition of the fractional Laplace operator and study a sparse optimal control problem involving a fractional, semilinear, and elliptic partial differential equation as state equation; control constraints…
The singularities that arise in elliptic boundary value problems are treated locally by a singular function boundary integral method. This method extracts the leading singular coefficients from a series expansion that describes the local…
This work is concerned with the optimal control problems governed by a 1D wave equation with variable coefficients and the control spaces $\mathcal M_T$ of either measure-valued functions $L_{w^*}^2(I,\mathcal M(\Omega))$ or vector measures…
For the optimal control problem governed by elliptic equations with interfaces, we present a numerical method based on the Hansbo's Nitsche-XFEM. We followed the Hinze's variational discretization concept to discretize the continuous…
We consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization. We provide a condition which allows to decide whether a solution of the necessary first order conditions is a global…
In this paper we apply an augmented Lagrange method to a class of semilinear elliptic optimal control problems with pointwise state constraints. We show strong convergence of subsequences of the primal variables to a local solution of the…
The article examines a linear-quadratic Neumann control problem that is governed by a non-coercive elliptic equation. Due to the non-self-adjoint nature of the linear control-to-state operator, it is necessary to independently study both…
The aim of this paper is twofold. On the one hand, we test numerically the performance of mixed virtual elements in three dimensions for the first time in the literature to solve the mixed formulation of three-dimensional elliptic equations…
We present multigrid methods for solving elliptic partial differential equations on arbitrary domains using the nodal ghost finite element method, an unfitted boundary approach where the domain is implicitly defined by a level-set function.…
This article develops variational integrators for a class of underactuated mechanical systems using the theory of discrete mechanics. Further, a discrete optimal control problem is formulated for the considered class of systems and…