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Dual Bernstein polynomials find many applications in approximation theory, computational mathematics, numerical analysis and computer-aided geometric design. In this context, one of the main problems is fast and accurate evaluation both of…

Numerical Analysis · Mathematics 2020-04-22 Filip Chudy , Paweł Woźny

We consider a control-constrained optimal control problem subject to time-harmonic Maxwell's equations; the control variable belongs to a finite-dimensional set and enters the state equation as a coefficient. We derive existence of optimal…

Numerical Analysis · Mathematics 2024-05-10 Francisco Fuica , Felipe Lepe , Pablo Venegas

A method is developed to numerically solve chance constrained optimal control problems. The chance constraints are reformulated as nonlinear constraints that retain the probability properties of the original constraint. The reformulation…

Optimization and Control · Mathematics 2020-05-29 Rachel E. Keil , Alexander T. Miller , Mrinal Kumar , Anil V. Rao

This paper deals with the merging problem of segments of a composite B\'ezier curve, with the endpoints continuity constraints. We present a novel method which is based on the idea of using constrained dual Bernstein polynomial basis (P.…

Numerical Analysis · Mathematics 2016-08-08 Paweł Woźny , Przemysław Gospodarczyk , Stanisław Lewanowicz

The problem of optimal motion planing and control is fundamental in robotics. However, this problem is intractable for continuous-time stochastic systems in general and the solution is difficult to approximate if non-instantaneous nonlinear…

Robotics · Computer Science 2017-02-28 Mustafa Mukadam , Ching-An Cheng , Xinyan Yan , Byron Boots

In this paper, we discuss the numerical approximation of a distributed optimal control problem governed by the von Karman equations, defined in polygonal domains with point-wise control constraints. Conforming finite elements are employed…

Numerical Analysis · Mathematics 2017-09-19 Gouranga Mallik , Neela Nataraj , Jean-Pierre Raymond

This paper details a methodology to transcribe an optimal control problem into a nonlinear program for generation of the trajectories that optimize a given functional by approximating only the highest order derivatives of a given system's…

Optimization and Control · Mathematics 2025-09-09 Thomas L. Ahrens , Ian M. Down , Manoranjan Majji

We provide a framework to approximate the 2-Wasserstein distance and the optimal transport map, amenable to efficient training as well as statistical and geometric analysis. With the quadratic cost and considering the Kantorovich dual form…

Optimization and Control · Mathematics 2019-02-20 Amirhossein Taghvaei , Amin Jalali

This paper is devoted to find the numerical solutions of one dimensional general nonlinear system of third-order boundary value problems (BVPs) for the pair of functions using Galerkin weighted residual method. We derive mathematical…

Numerical Analysis · Mathematics 2024-04-24 Snigdha Dhar , Md. Shafiqul Islam

A numerical study of an optimal control formulation for a shape optimization problem governed by an elliptic variational inequality is performed. The shape optimization problem is reformulated as a boundary control problem in a fixed…

Optimization and Control · Mathematics 2018-01-22 Raino A. E. Mäkinen

This the text of a proceeding accepted for the 21st International Symposium on Mathematical Theory of Networks and Systems (MTNS 2014). We present some results of an ongoing research on the controllability problem of an abstract bilinear…

Analysis of PDEs · Mathematics 2014-06-10 Nabile Boussaid , Marco Caponigro , Thomas Chambrion

In the context of optimal control, we consider the inverse problem of Lagrangian identification given system dynamics and optimal trajectories. Many of its theoretical and practical aspects are still open. Potential applications are very…

Optimization and Control · Mathematics 2014-03-21 Edouard Pauwels , Didier Henrion , Jean-Bernard Bernard Lasserre

Many problems of systems control theory boil down to solving polynomial equations, polynomial inequalities or polyomial differential equations. Recent advances in convex optimization and real algebraic geometry can be combined to generate…

Optimization and Control · Mathematics 2013-09-13 Didier Henrion

This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a…

Optimization and Control · Mathematics 2025-04-22 Yanzhao Cao , Hongjiang Qian , George Yin

Many uncertainty sets encountered in control systems analysis and design can be expressed in terms of semialgebraic sets, that is as the intersection of sets described by means of polynomial inequalities. Important examples are for instance…

Optimization and Control · Mathematics 2015-09-15 Fabrizio Dabbene , Didier Henrion , Constantino Lagoa

We obtain approximation results for general positive linear operators satisfying mild conditions, when acting on discontinuous functions and absolutely continuous functions having discontinuous derivatives. The upper bounds, given in terms…

Probability · Mathematics 2024-10-29 José A. Adell , P. Garrancho , F. J. Martínez-Sánchez

Oberman gave a stochastic control formulation of the problem of estimating the convex envelope of a non-convex function. Based on this, we develop a reinforcement learning scheme to approximate the convex envelope, using a variant of…

Systems and Control · Electrical Eng. & Systems 2023-11-27 Vivek S. Borkar , Adit Akarsh

Based on the stochastic maximum principle for the partially coupled forward-backward stochastic control system (FBSCS for short), a modified method of successive approximations (MSA for short) is established for stochastic recursive optimal…

Optimization and Control · Mathematics 2022-01-11 Shaolin Ji , Rundong Xu

We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time $(0,\epsilon)$-additive bicriteria approximation algorithm for finding optimal…

Data Structures and Algorithms · Computer Science 2025-02-12 Jeremy McMahan

The paper addresses an optimal control problem for a perturbed sweeping process of the rate-independent hysteresis type described by a controlled "play and stop" operator with separately controlled perturbations. This problem can be reduced…

Optimization and Control · Mathematics 2015-12-01 Tan H. Cao , Boris S. Mordukhovich