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Pseudospectral methods represent an efficient approach for solving optimal control problems. While Legendre-Gauss-Lobatto (LGL) collocation points have traditionally been considered inferior to Legendre-Gauss (LG) and Legendre-Gauss-Radau…

Systems and Control · Electrical Eng. & Systems 2025-07-03 Yilin Zou , Fanghua Jiang

The $hp$ local discontinuous Galerkin (LDG) method proposed by Castillo et al. [Math. Comp.,~71 (238): 455-478, 2002] has been shown to be an efficient approach for solving convection-diffusion equations. However, theoretical analysis…

Numerical Analysis · Mathematics 2026-03-05 Wenjie Liu , Ruiyi Xie , Li-Lian Wang , Zhimin Zhang

We investigate a numerical behaviour of robust deterministic optimal control problem subject to a convection diffusion equation containing uncertain inputs. Stochastic Galerkin approach, turning the original optimization problem containing…

Numerical Analysis · Mathematics 2023-03-01 Pelin Çiloğlu , Hamdullah Yücel

Motivated by the increasing availability of high-performance parallel computing, we design a distributed parallel algorithm for linearly-coupled block-structured nonconvex constrained optimization problems. Our algorithm performs…

Optimization and Control · Mathematics 2021-12-17 Anirudh Subramanyam , Youngdae Kim , Michel Schanen , François Pacaud , Mihai Anitescu

Motivated by broad applications in various fields of engineering, we study a network resource allocation problem where the goal is to optimally allocate a fixed quantity of resources over a network of nodes. We consider large scale networks…

Optimization and Control · Mathematics 2018-08-06 Thinh T. Doan , Carolyn L. Beck

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…

Numerical Analysis · Mathematics 2017-12-22 Bangti Jin , Buyang Li , Zhi Zhou

We design and compute a class of optimal control problems for reaction-diffusion systems. They form mean field control problems related to multi-density reaction-diffusion systems. To solve proposed optimal control problems numerically, we…

Optimization and Control · Mathematics 2023-06-13 Guosheng Fu , Stanley Osher , Will Pazner , Wuchen Li

The optimal controller design problem for a linear, first-order spatially-invariant distributed parameter system is considered. Through a case study of the Linear Quadratic Regulator (LQR) problem for the diffusion equation over the torus,…

Optimization and Control · Mathematics 2026-03-20 Addie McCurdy , Andrew Gusty , Emily Jensen

The DPG method with optimal test functions for solving linear quadratic optimal control problems with control constraints is studied. We prove existence of a unique optimal solution of the nonlinear discrete problem and characterize it…

Optimization and Control · Mathematics 2023-08-21 Thomas Führer , Francisco Fuica

We tackle a nonlinear optimal control problem for a stochastic differential equation in Euclidean space and its state-linear counterpart for the Fokker-Planck-Kolmogorov equation in the space of probabilities. Our approach is founded on a…

Optimization and Control · Mathematics 2024-09-23 Roman Chertovskih , Nikolay Pogodaev , Maxim Staritsyn , A. Pedro Aguiar

This technical note considers a distributed convex optimization problem with nonsmooth cost functions and coupled nonlinear inequality constraints. To solve the problem, we first propose a modified Lagrangian function containing local…

Optimization and Control · Mathematics 2017-05-09 Shu Liang , Xianlin Zeng , Yiguang Hong

We study a generalization of the classical discrete-time, Linear-Quadratic-Gaussian (LQG) control problem where the noise distributions affecting the states and observations are unknown and chosen adversarially from divergence-based…

Optimization and Control · Mathematics 2025-09-30 Bahar Taşkesen , Dan A. Iancu , Çağıl Koçyiğit , Daniel Kuhn

This paper investigates a symmetric dual-wind discontinuous Galerkin (DWDG) method for solving an elliptic optimal control problem with control constraints. The governing constraint is an elliptic partial differential equation (PDE), which…

Numerical Analysis · Mathematics 2025-06-17 Satyajith Bommana Boyana , Thomas Lewis , Sijing Liu , Yi Zhang

We propose a local discontinuous Galerkin (LDG) method for the fractional Korteweg-de Vries (KdV) equation, involving the fractional Laplacian with exponent $\alpha \in (1,2)$ in one and multiple space dimensions. By decomposing the…

Numerical Analysis · Mathematics 2024-11-19 Mukul Dwivedi , Tanmay Sarkar

In this work, we consider optimal control problems for mechanical systems on vector spaces with fixed initial and free final state and a quadratic Lagrange term. Specifically, the dynamics is described by a second order ODE containing an…

Anomalous diffusions are ubiquitous in nature, whose functional distributions are governed by the backward Feynman-Kac equation. In this paper, the local discontinuous Galerkin (LDG) method is used to solve the 2D backward Feynman-Kac…

Numerical Analysis · Mathematics 2022-06-01 Dong Liu , Weihua Deng

In this work, we analyse the discretisation of a recently proposed new Lagrangian approach to optimal control problems of affine-controlled second-order differential equations with cost functions quadratic in the controls. We propose exact…

Distributed optimization algorithms are used in a wide variety of problems involving complex network systems where the goal is for a set of agents in the network to solve a network-wide optimization problem via distributed update rules. In…

Optimization and Control · Mathematics 2025-09-23 Liam Hallinan , Ioannis Lestas

This paper introduces a generalization of the well-known Riccati recursion for solving the discrete-time equality-constrained linear quadratic optimal control problem. The recursion can be used to compute the solutions as well as optimal…

Optimization and Control · Mathematics 2024-12-31 Lander Vanroye , Joris De Schutter , Wilm Decré

We study an inverse problem of the stochastic optimal control of general diffusions with performance index having the quadratic penalty term of the control process. Under mild conditions on the system dynamics, the cost functions, and the…

Optimization and Control · Mathematics 2022-11-17 Yumiharu Nakano