Related papers: An intermediate targets method for time paralleliz…
We present variational theory for optimal control over a finite time interval in quantum systems with relaxation. The corresponding Euler-Lagrange equations determining the optimal control field are derived. In our theory the optimal…
We propose, analyze, and test new iterative solvers for large-scale systems of linear algebraic equations arising from the finite element discretization of reduced optimality systems defining the finite element approximations to the…
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…
We consider a general linear parabolic problem with extended time boundary conditions (including initial value problems and periodic ones), and approximate it by the implicit Euler scheme in time and the Gradient Discretisation method in…
In this contribution the usage of the Parareal method is proposed for the time-parallel solution of the eddy current problem. The method is adapted to the particular challenges of the problem that are related to the differential algebraic…
We present here the classical Schwarz method with a time domain decomposition applied to unconstrained parabolic optimal control problems. Unlike Dirichlet-Neumann and Neumann-Neumann algorithms, we find different properties based on the…
This paper is about a parallel algorithm for tube-based model predictive control. The proposed control algorithm solves robust model predictive control problems suboptimally, while exploiting their structure. This is achieved by…
Parallel-in-time methods are developed to accelerate the direct-adjoint looping procedure. Particularly, we utilize the Paraexp algorithm, previously developed to integrate equations forward in time, to accelerate the direct-adjoint looping…
We consider a semi-Lagrangian scheme for solving the minimum time problem, with a given target, and the associated eikonal type equation. We first use a discrete time deterministic optimal control problem interpretation of the time…
A geometric approach to kinematics in control theory is illustrated. A non-linear control system is derived for the problem and the Pontryagin maximum principle is used to find the time-optimal trajectories of the Parallel navigation. The…
In this paper, we consider the application of optimal periodic control sequences to switched dynamical systems. The control sequence is obtained using a finite-horizon optimal method based on dynamic programming. We then consider Euler…
We present a method for the numerical approximation of distributed optimal control problems constrained by parabolic partial differential equations. We complement the first-order optimality condition by a recently developed space-time…
This paper studies a time optimal control problem with control constraints of the rectangular type for the linear multi-input time-varying ordinary differential equations. The aims of this study are to establish certain necessary and…
The links between optimal control of dynamical systems and neural networks have proved beneficial both from a theoretical and from a practical point of view. Several researchers have exploited these links to investigate the stability of…
The applicability of the Parareal parallel-in-time integration scheme for the solution of a linear, two-dimensional hyperbolic acoustic-advection system, which is often used as a test case for integration schemes for numerical weather…
The analyses of interior penalty discontinuous Galerkin methods of any order k for solving elliptic and parabolic problems with Dirac line sources are presented. For the steady state case, we prove convergence of the method by deriving a…
In this work we study the asymptotic behavior of the solutions of a class of abstract parabolic time optimal control problems when the generators converge, in an appropriate sense, to a given strictly negative operator. Our main application…
In this paper we consider a parabolic optimal control problem with a Dirac type control with moving point source in two space dimensions. We discretize the problem with piecewise constant functions in time and continuous piecewise linear…
The time domain analysis of eddy current problems often requires the simulation of long time intervals, e.g. until a steady state is reached. Fast-switching excitations e.g. in pulsedwidth modulated signals require in addition very small…
In this note, we consider infinite horizon optimal control problems with deterministic systems. Since exact solutions to these problems are often intractable, we propose a parallel model predictive control (MPC) method that provides an…