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The paper is about the data-driven computation of optimal control for a class of control affine deterministic nonlinear systems. We assume that the control dynamical system model is not available, and the only information about the system…

Optimization and Control · Mathematics 2021-04-13 Bowen Huang , Umesh Vaidya

This paper presents a novel convex optimization-based method for finding the globally optimal solutions of a class of mixed-integer non-convex optimal control problems. We consider problems with non-convex constraints that restrict the…

Optimization and Control · Mathematics 2019-11-21 Danylo Malyuta , Behcet Acikmese

We consider the problem of finite-horizon optimal control design under uncertainty for imperfectly observed discrete-time systems with convex costs and constraints. It is known that this problem can be cast as an infinite-dimensional convex…

Optimization and Control · Mathematics 2019-04-02 Kevin J. Kircher , K. Max Zhang

This paper considers the stochastic linear quadratic optimal control problem in which the control domain is nonconvex. By the functional analysis and convex perturbation methods, we establish a novel maximum principle. The application of…

Optimization and Control · Mathematics 2017-11-01 Shaolin Ji , Xiaole Xue

In this work, we investigate the regularized solutions and their finite element solutions to the inverse source problems governed by partial differential equations, and establish the stochastic convergence and optimal finite element…

Numerical Analysis · Mathematics 2021-10-25 Zhiming Chen , Wenlong Zhang , Jun Zou

We consider an inverse problem involving the reconstruction of the solution to a nonlinear partial differential equation (PDE) with unknown boundary conditions. Instead of direct boundary data, we are provided with a large dataset of…

Numerical Analysis · Mathematics 2025-07-30 Erik Burman , Mats G. Larson , Karl Larsson , Carl Lundholm

The aim of this work is to derive a priori error estimates for finite element discretizations of control--constrained optimal control problems that involve the Stokes system and Dirac measures. The first problem entails the minimization of…

Numerical Analysis · Mathematics 2020-04-29 Francisco Fuica , Enrique Otarola , Daniel Quero

We introduce a max-plus analogue of the Petrov-Galerkin finite element method to solve finite horizon deterministic optimal control problems. The method relies on a max-plus variational formulation. We show that the error in the sup norm…

Optimization and Control · Mathematics 2009-12-13 Marianne Akian , Stephane Gaubert , Asma Lakhoua

This paper concerns an optimal control problem $(P)$ related to a nonlinear Fokker-Planck equation. The problem is deeply related to a stochastic optimal control problem $(P_S)$ for a McKean-Vlasov equation. The existence of an optimal…

Optimization and Control · Mathematics 2022-07-22 Stefana-Lucia Anita

We address the problem of computing a control for a time-dependent nonlinear system to reach a target set in a minimal time. To solve this minimal time control problem, we introduce a hierarchy of linear semi-infinite programs, the values…

Optimization and Control · Mathematics 2023-07-04 Antoine Oustry , Matteo Tacchi

In this paper, we propose a new approach to design globally convergent reduced-order observers for nonlinear control systems via contraction analysis and convex optimization. Despite the fact that contraction is a concept naturally suitable…

Optimization and Control · Mathematics 2021-08-17 Bowen Yi , Ruigang Wang , Ian R. Manchester

We consider a class of finite-horizon, linear-quadratic stochastic control problems, where the probability distribution governing the noise process is unknown but assumed to belong to an ambiguity set consisting of all distributions whose…

Optimization and Control · Mathematics 2026-04-21 Feras Al Taha , Eilyan Bitar

We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…

Numerical Analysis · Mathematics 2020-03-23 Ulrich Langer , Andreas Schafelner

We study a non-local optimal control problem involving a linear, bond-based peridynamics model. In addition to existence and uniqueness of solutions to our problem, we investigate their behavior as the horizon parameter $\delta$, which…

Optimization and Control · Mathematics 2023-04-20 Tadele Mengesha , Abner J. Salgado , Joshua M. Siktar

We consider a continuous time stochastic optimal control problem under both equality and inequality constraints on the expectation of some functionals of the controlled process. Under a qualification condition, we show that the problem is…

Optimization and Control · Mathematics 2021-07-09 Laurent Pfeiffer , Xiaolu Tan , Yulong Zhou

This paper addresses the problem of control synthesis for nonlinear optimal control problems in the presence of state and input constraints. The presented approach relies upon transforming the given problem into an infinite-dimensional…

Optimization and Control · Mathematics 2017-03-03 Pengcheng Zhao , Shankar Mohan , Ram Vasudevan

This article deals with error estimates for the finite element approximation of variational normal derivatives and, as a consequence, error estimates for the finite element approximation of Dirichlet boundary control problems with energy…

Numerical Analysis · Mathematics 2018-08-06 Max Winkler

We consider standard tracking-type, distributed elliptic optimal control problems with $L^2$ regularization, and their finite element discretization. We are investigating the $L^2$ error between the finite element approximation $u_{\varrho…

Numerical Analysis · Mathematics 2022-07-12 Ulrich Langer , Richard Löscher , Olaf Steinbach , Huidong Yang

In this article, we consider parabolic equations on a bounded open connected subset $\Omega$ of $\R^n$. We model and investigate the problem of optimal shape and location of the observation domain having a prescribed measure. This problem…

Optimization and Control · Mathematics 2015-06-19 Yannick Privat , Emmanuel Trélat , Enrique Zuazua

We study a linear-quadratic optimal control problem involving a parabolic equation with fractional diffusion and Caputo fractional time derivative of orders $s \in (0,1)$ and $\gamma \in (0,1]$, respectively. The spatial fractional…

Optimization and Control · Mathematics 2015-04-02 Harbir Antil , Enrique Otarola , Abner J. Salgado