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In this paper we propose a method to improve the accuracy of trajectory optimization for dynamic robots with intermittent contact by using orthogonal collocation. Until recently, most trajectory optimization methods for systems with…

Robotics · Computer Science 2019-04-03 Amir Patel , Stacey Shield , Saif Kazi , Aaron M. Johnson , Lorenz T. Biegler

This paper discusses a method enabling optimal control of nonlinear systems that are subject to parametric uncertainty. A stochastic optimal tracking problem is formulated that can be expressed in function of the first two stochastic…

Optimization and Control · Mathematics 2018-08-22 Tom Lefebvre , Frederik De Belie , Guillaume Crevecoeur

Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…

Optimization and Control · Mathematics 2024-12-30 Tobias Breiten , Shubhaditya Burela , Philipp Schulze

Solving optimal control problems for transport-dominated partial differential equations (PDEs) can become computationally expensive, especially when dealing with high-dimensional systems. To overcome this challenge, we focus on developing…

Optimization and Control · Mathematics 2026-03-31 Tobias Breiten , Shubhaditya Burela , Philipp Schulze

An effective method to obtain exact analytical solutions of equations describing the coherent dynamics of multilevel systems is presented. The method is based on the usage of orthogonal polynomials, integral transforms and their discrete…

Classical Analysis and ODEs · Mathematics 2007-05-23 V. A. Savva , V. I. Zelenkov , A. S. Mazurenko

Reduced basis approximations of Optimal Control Problems (OCPs) governed by steady partial differential equations (PDEs) with random parametric inputs are analyzed and constructed. Such approximations are based on a Reduced Order Model,…

Numerical Analysis · Mathematics 2023-08-08 Giuseppe Carere , Maria Strazzullo , Francesco Ballarin , Gianluigi Rozza , Rob Stevenson

This paper focuses on optimal control problem for a class of discrete-time nonlinear systems. In practical applications, computation time is a crucial consideration when solving nonlinear optimal control problems, especially under real-time…

Optimization and Control · Mathematics 2025-04-01 Chuanzhi Lv , Xunmin Yin , Hongdan Li , Huanshui Zhang

We introduce a modeling framework for manipulation planning based on the formulation of the dynamics as a projected dynamical system. This method uses implicit signed distance functions and their gradients to formulate an equivalent…

Optimization and Control · Mathematics 2025-01-22 Anton Pozharskiy , Armin Nurkanović , Moritz Diehl

Direct methods for the simulation of optimal control problems apply a specific discretization to the dynamics of the problem, and the discrete adjoint method is suitable to calculate corresponding conditions to approximate an optimal…

We derive novel algorithms for optimization problems constrained by partial differential equations describing multiscale particle dynamics, including non-local integral terms representing interactions between particles. In particular, we…

Numerical Analysis · Mathematics 2021-09-09 Mildred Aduamoah , Benjamin D. Goddard , John W. Pearson , Jonna C. Roden

We propose an approach to trajectory optimization for piecewise polynomial systems based on the recently proposed graphs of convex sets framework. We instantiate the framework with a convex relaxation of optimal control based on occupation…

Optimization and Control · Mathematics 2025-07-28 Etienne Buehrle , Ömer Şahin Taş , Christoph Stiller

Standard optimal control methods perform optimization in the time domain. However, many experimental settings demand the expression of the control signal as a superposition of given waveforms, a case that cannot easily be accommodated using…

Optimization and Control · Mathematics 2015-06-22 Selina Meister , Jürgen T. Stockburger , Rebecca Schmidt , Joachim Ankerhold

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

In this article, we discuss two algorithms tailored to discrete-time deterministic finite-horizon nonlinear optimal control problems or so-called deterministic trajectory optimization problems. Both algorithms can be derived from an…

Optimization and Control · Mathematics 2024-12-10 Mohammad Mahmoudi Filabadi , Tom Lefebvre , Guillaume Crevecoeur

In this paper, we propose a Transformer-based framework for approximating solutions to infinite-dimensional optimization problems: calculus of variations problems and optimal control problems. Our approach leverages offline training on data…

Optimization and Control · Mathematics 2025-11-20 Gage MacLin , Venanzio Cichella , Andrew Patterson , Irene Gregory

We consider nonlinear optimal control problems (OCPs) for which all problem data are polynomial. In the first part of the paper, we review how occupation measures can be used to approximate pointwise the optimal value function of a given…

Optimization and Control · Mathematics 2008-12-18 Didier Henrion , Jean B. Lasserre , Carlo Savorgnan

We propose a spectral collocation method to approximate the exact boundary control of the wave equation in a square domain. The idea is to introduce a suitable approximate control problem that we solve in the finite-dimensional space of…

Numerical Analysis · Mathematics 2023-04-17 Somia Boumimez , Carlos Castro

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 present an approach for solving optimal Dirichlet boundary control problems of nonlinear optics by using deep learning. For computing high resolution approximations of the solution to the nonlinear wave model, we propose higher order…

Numerical Analysis · Mathematics 2023-12-27 Nils Margenberg , Franz X. Kärtner , Markus Bause

This work presents a novel algorithm for impulsive optimal control of linear time-varying systems with the inclusion of input magnitude constraints. Impulsive optimal control problems, where the optimal input solution is a sum of delta…

Optimization and Control · Mathematics 2026-03-17 Ethan Foss , Simone D'Amico