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This paper is concerned with the distributed control and stabilization problems for linear discrete-time large scale systems with imposed constraints. The main contributions of this paper are: Firstly, by using the maximum principle…

Optimization and Control · Mathematics 2018-01-03 Qingyuan Qi , Huanshui Zhang , Peijun Ju

The goal of this paper is to solve a class of stochastic optimal control problems numerically, in which the state process is governed by an It\^o type stochastic differential equation with control process entering both in the drift and the…

Optimization and Control · Mathematics 2020-06-05 Richard Archibald , Feng Bao , Jiongmin Yong , Tao Zhou

We investigate a second-order accurate time-stepping scheme for solving a time-fractional diffusion equation with a Caputo derivative of order~$\alpha \in (0,1)$. The basic idea of our scheme is based on local integration followed by linear…

Numerical Analysis · Mathematics 2024-07-10 Kassem Mustapha , William McLean , Josef Dick

We characterize the optimal control for a class of singular stochastic control problems as the unique solution to a related Skorokhod reflection problem. The considered optimization problems concern the minimization of a discounted cost…

Optimization and Control · Mathematics 2023-05-22 Jodi Dianetti , Giorgio Ferrari

We propose and analyze an a posteriori error estimator for a PDE-constrained optimization problem involving a nondifferentiable cost functional, fractional diffusion, and control-constraints. We realize fractional diffusion as the…

Numerical Analysis · Mathematics 2019-06-04 Enrique Otarola

Optimal control problems are inherently hard to solve as the optimization must be performed simultaneously with updating the underlying system. Starting from an initial guess, Howard's policy improvement algorithm separates the step of…

Optimization and Control · Mathematics 2020-05-25 B. Kerimkulov , D. Šiška , Ł. Szpruch

We present a formulation of an optimal control problem for a two-dimensional diffusion process governed by a Fokker-Planck equation to achieve a nonequilibrium steady state with a desired circulation while accelerating convergence toward…

Systems and Control · Electrical Eng. & Systems 2026-03-26 Norihisa Namura , Hiroya Nakao

We formulate and analyse an optimal control problem for the coagulation-fragmentation equation, where a scalar, time-dependent control modulates the coagulation rate by multiplying the coagulation kernel. The objective functional consists…

Optimization and Control · Mathematics 2026-04-16 Enrico Sartor

We consider a simple initial-boundary-value problem for the shallow water equations in one space dimension, and also the analogous problem for a symmetric variant of the system. Assuming smoothness of solutions, we discretize these problems…

Numerical Analysis · Mathematics 2014-11-26 D. C. Antonopoulos , V. A. Dougalis

The paper focuses on unconditionally optimal error analysis of the fully discrete Galerkin finite element methods for a general nonlinear parabolic system in $\R^d$ with $d=2,3$. In terms of a corresponding time-discrete system of PDEs as…

Numerical Analysis · Mathematics 2013-03-27 Buyang Li , Weiwei Sun

In this contribution we propose reduced order methods to fast and reliably solve parametrized optimal control problems governed by time dependent nonlinear partial differential equations. Our goal is to provide a tool to deal with the time…

Numerical Analysis · Mathematics 2023-08-08 Francesco Ballarin , Gianluigi Rozza , Maria Strazzullo

The optimal control of problems that are constrained by partial differential equations with uncertainties and with uncertain controls is addressed. The Lagrangian that defines the problem is postulated in terms of stochastic functions, with…

Optimization and Control · Mathematics 2012-11-19 Eveline Rosseel , Garth N. Wells

We propose an embedded discontinuous Galerkin (EDG) method to approximate the solution of a distributed control problem governed by convection diffusion PDEs, and obtain optimal a priori error estimates for the state, dual state, their…

Numerical Analysis · Mathematics 2019-06-04 Xiao Zhang , Yangwen Zhang , John R. Singler

The paper is devoted to the study of a new class of optimal control problems governed by discontinuous constrained differential inclusions of the sweeping type with involving the duration of the dynamic process into optimization. We develop…

Optimization and Control · Mathematics 2023-10-18 Giovanni Colombo , Boris S. Mordukhovich , Dao Nguyen , Trang Nguyen

We show that, for any spatially discretized system of reaction-diffusion, the approximate solution given by the explicit Euler time-discretization scheme converges to the exact time-continuous solution, provided that diffusion coefficient…

Optimization and Control · Mathematics 2019-12-12 Adrien Le Coënt , Laurent Fribourg

In this paper we discuss the numerical solution of elliptic distributed optimal control problems with state or control constraints when the control is considered in the energy norm. As in the unconstrained case we can relate the…

Numerical Analysis · Mathematics 2023-06-28 Peter Gangl , Richard Löscher , Olaf Steinbach

In this paper, we consider optimal control problems derived by stochastic systems with delay, where control domains are non-convex and the diffusion coefficients depend on control variables. By an estimate of the integral of…

Optimization and Control · Mathematics 2022-10-25 Qixia Zhang

This paper is concerned with an optimal control problem subject to the $H^1$-critical defocusing semilinear wave equation on a smooth and bounded domain in three spatial dimensions. Due to the criticality of the nonlinearity in the wave…

Optimization and Control · Mathematics 2019-07-08 Karl Kunisch , Hannes Meinlschmidt

This paper is devoted to the distributed continuous-time optimization problem with time-varying objective functions and time-varying nonlinear inequality constraints. Different from most studied distributed optimization problems with…

Optimization and Control · Mathematics 2020-09-08 Shan Sun , Wei Ren

An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…

Optimization and Control · Mathematics 2026-03-18 Alexander M. Davies , Sara Pollock , Miriam E. Dennis , Anil V. Rao