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In this paper, optimal control problems governed by diffusion equations with Dirichlet and Neumann boundary conditions are investigated in the framework of the gradient discretisation method. Gradient schemes are defined for the optimality…
In this study, we introduce numerical methods for discretizing continuous-time linear-quadratic optimal control problems (LQ-OCPs). The discretization of continuous-time LQ-OCPs is formulated into differential equation systems, and we can…
This study focuses on the numerical discretization methods for the continuous-time discounted linear-quadratic optimal control problem (LQ-OCP) with time delays. By assuming piecewise constant inputs, we formulate the discrete system…
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 consider a pointwise tracking optimal control problem for a semilinear elliptic partial differential equation. We derive the existence of optimal solutions and analyze first and, necessary and sufficient, second order optimality…
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…
Appropriate time discretization is crucial for real-time applications of numerical optimal control, such as nonlinear model predictive control. However, if the discretization error strongly depends on the applied control input, meeting…
We present an optimize-then-discretize framework for solving linear-quadratic optimal control problems (OCP) governed by time-inhomogeneous ordinary differential equations (ODEs). Our method employs a modified overlapping Schwarz…
The scope of this paper is the analysis and approximation of an optimal control problem related to the Allen-Cahn equation. A tracking functional is minimized subject to the Allen-Cahn equation using distributed controls that satisfy…
We study the numerical approximation of linear-quadratic optimal control problems subject to the fractional Laplace equation with its spectral definition. We compute an approximation of the state equation using a discretization of the…
This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time…
A proof of optimal-order error estimates is given for the full discretization of the Cahn--Hilliard equation with Cahn--Hilliard-type dynamic boundary conditions in a smooth domain. The numerical method combines a linear bulk--surface…
This paper studies an optimal control problem governed by a semilinear elliptic equation, in which the control acts in a multiplicative or bilinear way as the reaction coefficient of the equation. We focus on the numerical discretization of…
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…
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…
This paper presents the numerical discretization methods of the continuous-time linear-quadratic optimal control problems (LQ-OCPs) with time delays. We describe the weight matrices of the LQ-OCPs as differential equations systems, allowing…
We investigate $C^1$ finite element methods for one dimensional elliptic distributed optimal control problems with pointwise constraints on the derivative of the state formulated as fourth order variational inequalities for the state…
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…
In this paper, we investigate a distributed optimal control problem for a convective viscous Cahn-Hilliard system with dynamic boundary conditions. Such systems govern phase separation processes between two phases taking place in an…
We propose and analyze a new discretization technique for a linear-quadratic optimal control problem involving the fractional powers of a symmetric and uniformly elliptic second oder operator; control constraints are considered. Since these…