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The challenge of mastering computational tasks of enormous size tends to frequently override questioning the quality of the numerical outcome in terms of accuracy. By this we do not mean the accuracy within the discrete setting, which…

Numerical Analysis · Mathematics 2019-10-17 Markus Bachmayr , Wolfgang Dahmen

Safety is one of the fundamental challenges in control theory. Recently, multi-step optimal control problems for discrete-time dynamical systems were formulated to enforce stability, while subject to input constraints as well as…

Optimization and Control · Mathematics 2023-07-14 Shuo Liu , Jun Zeng , Koushil Sreenath , Calin A. Belta

An optimal control problem related to the probability of transition between stable states for a thermally driven Ginzburg-Landau equation is considered. The value function for the optimal control problem with a spatial discretization is…

Optimization and Control · Mathematics 2008-09-11 Mattias Sandberg

This paper investigates the central role played by the Hamiltonian in continuous-time nonlinear optimal control problems. We show that the strict convexity of the Hamiltonian in the control variable is a sufficient condition for the…

Optimization and Control · Mathematics 2024-04-15 Abhijeet , Mohamed Naveed Gul Mohamed , Aayushman Sharma , Suman Chakravorty

The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled "play and stop" operator with separately controlled perturbations. This problem can be reduced…

Optimization and Control · Mathematics 2015-12-01 Tan H. Cao , Boris S. Mordukhovich

This paper examines stochastic optimal control problems in which the state is perfectly known, but the controller's measure of time is a stochastic process derived from a strictly increasing L\'evy process. We provide dynamic programming…

Optimization and Control · Mathematics 2014-01-03 Andrew Lamperski , Noah J. Cowan

In [1] we consider an optimal control problem subject to a semilinear elliptic PDE together with its variational discretization, where we provide a condition which allows to decide whether a solution of the necessary first order conditions…

Optimization and Control · Mathematics 2017-05-04 Ahmad Ahmad Ali , Klaus Deckelnick , Michael Hinze

This paper studies the well-posedness and regularity of safe stabilizing optimization-based controllers for control-affine systems in the presence of model uncertainty. When the system dynamics contain unknown parameters, a finite set of…

Optimization and Control · Mathematics 2024-01-01 Pol Mestres , Kehan Long , Nikolay Atanasov , Jorge Cortés

The paper presents an approach to studying optimal control problems in the space of nonnegative measures with dynamics given by a nonlocal balance law. This approach relies on transforming the balance law into a continuity equation in the…

Optimization and Control · Mathematics 2025-01-30 Nikolay Pogodaev , Maxim Staritsyn

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,…

Numerical Analysis · Mathematics 2025-12-11 Christos Pervolianakis

In this paper we consider a method of solving optimal stopping problems in discrete and continuous time based on their dual representation. A novel and generic simulation-based optimization algorithm not involving nested simulations is…

Probability · Mathematics 2013-09-10 Denis Belomestny

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…

Optimization and Control · Mathematics 2014-02-04 Ramanarayan Vasudevan , Humberto Gonzalez , Ruzena Bajcsy , S. Shankar Sastry

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…

Optimization and Control · Mathematics 2020-06-24 Christian Glusa , Enrique Otarola

In this paper we design a novel class of online distributed optimization algorithms leveraging control theoretical techniques. We start by focusing on quadratic costs, and assuming to know an internal model of their variation. In this…

Optimization and Control · Mathematics 2026-01-21 Wouter J. A. van Weerelt , Nicola Bastianello

We consider some boundary value tracking optimal control problem constrained by a Neumann boundary value problem for some elliptic partial differential equation where the control acts as right-hand side. This optimal control problem can be…

Numerical Analysis · Mathematics 2026-03-12 Ulrich Langer , Richard Löscher , Olaf Steinbach , Huidong Yang

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…

Optimization and Control · Mathematics 2015-02-09 Marius Tucsnak , Gengsheng Wang , Chi-Ting Wu

This paper presents an algorithm to solve non-convex optimal control problems, where non-convexity can arise from nonlinear dynamics, and non-convex state and control constraints. This paper assumes that the state and control constraints…

Optimization and Control · Mathematics 2017-05-05 Yuanqi Mao , Michael Szmuk , Behcet Acikmese

We focus on optimal control problems governed by elliptic, quasilinear PDEs. Though there are various examples of such problems in the literature, we make an attempt at describing some general principles by dealing with three basic…

Optimization and Control · Mathematics 2024-01-22 Pablo Pedregal

For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its solution. We justify the presence of non-physical oscillations…

Numerical Analysis · Mathematics 2026-01-15 Constantin Bacuta

We introduce a numerical technique for controlling the location and stability properties of Hopf bifurcations in dynamical systems. The algorithm consists of solving an optimization problem constrained by an extended system of nonlinear…

Numerical Analysis · Mathematics 2023-09-20 Nicolas Boullé , Patrick E. Farrell , Marie E. Rognes