Related papers: A Neumann interface optimal control problem with e…
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…
Solving nonlinear optimal control problems is a challenging task, particularly for high-dimensional problems. We propose algorithms for model-based policy iterations to solve nonlinear optimal control problems with convergence guarantees.…
We adopt the integral definition of the fractional Laplace operator and analyze solution techniques for fractional, semilinear, and elliptic optimal control problems posed on Lipschitz polytopes. We consider two strategies of…
We consider the optimal control of singular nonlinear partial differential equation which is the distributional formulation of the multiphase Stefan type free boundary problem for the general second order parabolic equation. Boundary heat…
The purpose of this work is to study an optimal control problem for a semilinear elliptic partial differential equation with a linear combination of Dirac measures as a forcing term; the control variable corresponds to the amplitude of such…
Stability and optimal convergence analysis of a non-uniform implicit-explicit L1 finite element method (IMEX-L1-FEM) is studied for a class of time-fractional linear partial differential/integro-differential equations with non-self-adjoint…
We propose an {\em implementable} numerical scheme for the discretization of linear-quadratic optimal control problems involving SDEs in higher dimensions with {\em control constraint}. For time discretization, we employ the implicit Euler…
This work proposes an $r$-adaptive finite element method (FEM) using neural networks (NNs). The method employs the Ritz energy functional as the loss function, currently limiting its applicability to symmetric and coercive problems, such as…
In this work, an adaptive edge element method is developed for an H(curl)-elliptic constrained optimal control problem. We use the lowest-order Nedelec's edge elements of first family and the piecewise (element-wise) constant functions to…
In the past decade, a combination of unfitted finite elements (or XFEM) with the Nitsche method has become a popular discretization method for elliptic interface problems. This development started with the introduction and analysis of this…
Optimal control for switch-based dynamical systems is a challenging problem in the process control literature. In this study, we model these systems as hybrid dynamical systems with finite number of unknown switching points and reformulate…
We derive error estimates for a linear-quadratic elliptic distributed optimal control problem with pointwise control constraints that can be applied to standard finite element methods and multiscale finite element methods.
This paper analyzes two eXtended finite element methods (XFEMs) for linear quadratic optimal control problems governed by Poisson equation in non-convex domains. We follow the variational discretization concept to discretize the continuous…
We consider the inverse multiphase Stefan problem, where information on the heat flux on the fixed boundary is missing and must be found along with the temperature and free boundaries. Optimal control framework is pursued, where boundary…
We investigate the application of a posteriori error estimates to a fractional optimal control problem with pointwise control constraints. Specifically, we address a problem in which the state equation is formulated as an integral form of…
The study of optimal control problems under uncertainty plays an important role in scientific numerical simulations. This class of optimization problems is strongly utilized in engineering, biology and finance. In this paper, a stochastic…
This article presents an error analysis of the recently introduced Frenet immersed finite element (IFE) method. The Frenet IFE space employed in this method is constructed to be locally conforming to the function space of the associated…
In this paper, we present a new numerical method for determining the numerical solution of interface problems to optimal accuracy with respect to the polynomial order of the Lagrangian finite element space on polytopial meshes. We introduce…
In this article a special class of nonlinear optimal control problems involving a bilinear term in the boundary condition is studied. These kind of problems arise for instance in the identification of an unknown space-dependent Robin…
We analyze an optimal control problem with pointwise tracking for a fractional semilinear elliptic partial differential equation. The diffusion is characterized by the spectral fractional Laplacian $(-\Delta)^s$ with $s \in (1/2,1)$, a…