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The paper addresses the exact linearization of flat nonlinear discrete-time systems by generalized static or dynamic feedbacks which may also depend on forward-shifts of the new input. We first investigate the question which forward-shifts…

Optimization and Control · Mathematics 2022-12-29 Bernd Kolar , Johannes Diwold , Conrad Gstöttner , Markus Schöberl

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

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

We optimize the path of a mobile sensor to minimize the posterior uncertainty of a Bayesian inverse problem. Along its path, the sensor continuously takes measurements of the state, which is a physical quantity modeled as the solution of a…

Computational Engineering, Finance, and Science · Computer Science 2025-09-22 Nicole Aretz , Thomas Lynn , Karen Willcox , Sven Leyffer

Motion planning and control are two core components of the robotic systems autonomy stack. The standard approach to combine these methodologies comprises an offline/open-loop stage, planning, that designs a feasible and safe trajectory to…

Systems and Control · Electrical Eng. & Systems 2023-10-23 Tianqi Zheng , John W. Simpson-Porco , Enrique Mallada

Optimal control of the singular nonlinear parabolic PDE which is a distributional formulation of multidimensional and multiphase Stefan-type free boundary problem is analyzed. Approximating sequence of finite-dimensional optimal control…

Analysis of PDEs · Mathematics 2020-06-16 Ugur G. Abdulla , Evan Cosgrove

This work addresses an optimal control problem constrained by a degenerate kinetic equation of parabolic-hyperbolic type. Using a hypocoercivity framework we establish the well-posedness of the problem and demonstrate that the optimal…

Numerical Analysis · Mathematics 2024-12-17 Aaron Pim , Tristan Pryer , Alex Trenam

We consider the optimal control problem of a general nonlinear spatio-temporal system described by Partial Differential Equations (PDEs). Theory and algorithms for control of spatio-temporal systems are of rising interest among the…

Optimization and Control · Mathematics 2021-04-12 Ethan N. Evans , Oswin So , Andrew P. Kendall , Guan-Horng Liu , Evangelos A. Theodorou

In this paper, uniformly unconditionally stable first and second order finite difference schemes are developed for kinetic transport equations in the diffusive scaling. We first derive an approximate evolution equation for the macroscopic…

Numerical Analysis · Mathematics 2022-11-10 Guoliang Zhang , Hongqiang Zhu , Tao Xiong

This paper develops and analyzes a semi-discrete and a fully discrete finite element method for a one-dimensional quasilinear parabolic stochastic partial differential equation (SPDE) which describes the stochastic mean curvature flow for…

Numerical Analysis · Mathematics 2013-03-26 Xiaobing Feng , Yukun Li , Andreas Prohl

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

When planning motions in a configuration space that has underlying symmetries (e.g. when manipulating one or multiple symmetric objects), the ideal planning algorithm should take advantage of those symmetries to produce shorter…

Robotics · Computer Science 2025-07-18 Thomas Cohn , Russ Tedrake

We study the navigation problem for a robot moving amidst static and dynamic obstacles and rely on a hierarchical approach to solve it. First, the reference trajectory is planned by the safe interval path planning algorithm that is capable…

Robotics · Computer Science 2019-06-18 Konstantin Yakovlev , Anton Andreychuk , Juliya Belinskaya , Dmitry Makarov

In this series of papers, we present a motion planning framework for planning comfortable and customizable motion of nonholonomic mobile robots such as intelligent wheelchairs and autonomous cars. In this first one we present the…

Robotics · Computer Science 2013-05-23 Shilpa Gulati , Chetan Jhurani , Benjamin Kuipers

The paper presents the first rigorous error analysis of an unfitted finite element method for a linear parabolic problem posed on an evolving domain $\Omega(t)$ that may undergo a topological change, such as, for example, a domain…

Numerical Analysis · Mathematics 2026-01-28 Maxim A. Olshanskii , Arnold Reusken

A physical nonlinear dynamical model of a laser diode is considered. We propose a feed-forward control scheme based on differential flatness for the design of input-current modulations to compensate diode distortions. The goal is to…

Optimization and Control · Mathematics 2007-09-25 A. Abichou S. Elasmi P. Rouchon

The paper considers the problem of constructing program control for an object described by a system with a quasidifferentiable right-hand side. The control aim is to bring the system from a given initial position to a given final state in…

Optimization and Control · Mathematics 2025-11-17 Alexander Fominyh

We consider the task of motion control for non-prehensile manipulation using parallel kinematics mechatronic setup, in particular, stabilization of a ball on a plate under unmeasured external harmonic disturbances. System parameters are…

Systems and Control · Electrical Eng. & Systems 2020-05-19 Dmitrii Dobriborsci , Sergey Kolyubin , Alexey Bobtsov

A method is presented for the numerical solution of optimal boundary control problems governed by parabolic partial differential equations. The continuous space-time optimal control problem is transcribed into a sparse nonlinear programming…

Optimization and Control · Mathematics 2026-03-17 Alexander M. Davies , Sara Pollock , Miriam E. Dennis , Anil V. Rao

Although there is a substantial body of literature on control and optimization problems for parabolic and hyperbolic systems, the specific problem of controlling and optimizing the coefficients of the associated operators within such…

Optimization and Control · Mathematics 2026-05-21 Alain Bensoussan , Minh-Binh Tran , Bangjie Wang