Control theory | Numerical analysis | Optimal control

Legendre pseudospectral method

The Legendre pseudospectral method for optimal control problems is based on Legendre polynomials. It is part of the larger theory of pseudospectral optimal control, a term coined by Ross. A basic version of the Legendre pseudospectral was originally proposed by Elnagar and his coworkers in 1995. Since then, Ross, Fahroo and their coworkers have extended, generalized and applied the method for a large range of problems. An application that has received wide publicity is the use of their method for generating real time trajectories for the International Space Station. (Wikipedia).

Video thumbnail

Legendre Polynomials

An introduction to Legendre Polynomials and the Legendre-Fourier Series.

From playlist Mathematical Physics II Uploads

Video thumbnail

Legendre Series Example

An example of expanding a function in a Legendre-Fourier Series.

From playlist Mathematical Physics II Uploads

Video thumbnail

Intro to Legendre Polynomials

In this video I briefly introduce Legendre Polynomials via the Rodrigues formula. For more videos on this topic, visit: https://www.youtube.com/playlist?list=PL2uXHjNuf12bnpcGIOY2ZOsF-kl2Fh55F

From playlist Fourier

Video thumbnail

Legendre Polynomial Series

In this video I derive three series representations for Legendre Polynomials. For more videos on this topic, visit: https://www.youtube.com/playlist?list=PL2uXHjNuf12bnpcGIOY2ZOsF-kl2Fh55F

From playlist Fourier

Video thumbnail

[Calculus] Newton's Method || Lecture 36

Visit my website: http://bit.ly/1zBPlvm Subscribe on YouTube: http://bit.ly/1vWiRxW Hello, welcome to TheTrevTutor. I'm here to help you learn your college courses in an easy, efficient manner. If you like what you see, feel free to subscribe and follow me for updates. If you have any que

From playlist Calculus 1

Video thumbnail

The 3D Axisymmetric Euler Equation: A Pseudospectral Investigation of a... by Rahul Pandit

PROGRAM TURBULENCE: PROBLEMS AT THE INTERFACE OF MATHEMATICS AND PHYSICS ORGANIZERS Uriel Frisch (Observatoire de la Côte d'Azur and CNRS, France), Konstantin Khanin (University of Toronto, Canada) and Rahul Pandit (IISc, India) DATE & TIME 16 January 2023 to 27 January 2023 VENUE Ramanuj

From playlist Turbulence: Problems at the Interface of Mathematics and Physics 2023

Video thumbnail

Gaussian Quadrature | Lecture 40 | Numerical Methods for Engineers

An explanation of Gaussian quadrature. An example of how to calculate the weights and nodes for two-point Legendre-Gauss quadrature. Join me on Coursera: https://www.coursera.org/learn/numerical-methods-engineers Lecture notes at http://www.math.ust.hk/~machas/numerical-methods-for-engi

From playlist Numerical Methods for Engineers

Video thumbnail

A (Potential) Finite-Time Singularity and Thermalization in the 3D Axisymmetric... by Rahul Pandit

DISCUSSION MEETING : STATISTICAL PHYSICS OF COMPLEX SYSTEMS ORGANIZERS : Sumedha (NISER, India), Abhishek Dhar (ICTS-TIFR, India), Satya Majumdar (University of Paris-Saclay, France), R Rajesh (IMSc, India), Sanjib Sabhapandit (RRI, India) and Tridib Sadhu (TIFR, India) DATE : 19 December

From playlist Statistical Physics of Complex Systems - 2022

Video thumbnail

How To Use Newton's Method

Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys How To Use Newton's Method from Calculus. An easy example using the formula.

From playlist Calculus

Video thumbnail

Using de Moivre's Theorem - example question (2 of 2: Purely imaginary)

More resources available at www.misterwootube.com

From playlist Using Complex Numbers

Video thumbnail

[Lesson 25] QED Prerequisites Scattering 2

We follow the derivation of the associated Legendre polynomials using the reference "The Functions of Mathematical Physics" by Harry Hochstadt as our guide. The goal is to take ownership of these functions so we can confidently advance our understanding of the partial wave expansion of pla

From playlist QED- Prerequisite Topics

Video thumbnail

"How to Verify the Riemann Hypothesis for the First 1,000 Zeta Zeros" by Ghaith Hiary

An overview of algorithms and methods that mathematicians in the 19th century and the first half of the 20th century used to verify the Riemann hypothesis. The resulting numerical computations, which used hand calculations and mechanical calculators, include those by Gram, Lindelöf, Backlu

From playlist Number Theory Research Unit at CAMS - AUB

Video thumbnail

QED Prerequisites-Scattering 8-PartialWaves!

This lesson covers the amazing topic of expanding plane waves into a superposition of partial waves. To do this we will deploy the asymptotic expansion of the spherical Bessel function that we derived in previous lessons AND learn a quick and easy way to get the asymptotic expansion of cer

From playlist QED- Prerequisite Topics

Video thumbnail

Mirror symmetry for the trefoil knot - Emmy Murphy

Workshop on Homological Mirror Symmetry: Methods and Structures Speaker:Emmy Murphy Title: Mirror symmetry for the trefoil knot Affilation: MIT Date: November 9, 2016 For more vide, visit http://video.ias.edu

From playlist Workshop on Homological Mirror Symmetry: Methods and Structures

Video thumbnail

Iteration

Powered by https://www.numerise.com/ Iteration

From playlist Numerical Methods

Video thumbnail

C0 contact geometry of isotropic submanifolds - Maksim Stokić

Joint IAS/Princeton/Montreal/Paris/Tel-Aviv Symplectic Geometry Zoominar Three 20-minute research talks Topic: C0 contact geometry of isotropic submanifolds Speaker: Maksim Stokić Affiliation: Tel Aviv University Date: May 27, 2022  Homeomorphism is called contact if it can be written a

From playlist Mathematics

Video thumbnail

Knot contact homology and partially wrapped Floer homology - Lenhard Ng

Workshop on Homological Mirror Symmetry: Methods and Structures Speaker:Lenhard Ng Title: Knot contact homology and partially wrapped Floer homology Affilation: Duke Date: November 7, 2016 For more vide, visit http://video.ias.edu

From playlist Workshop on Homological Mirror Symmetry: Methods and Structures

Video thumbnail

Solving a trigonometric equation with applying pythagorean identity

👉 Learn how to solve trigonometric equations. There are various methods that can be used to evaluate trigonometric equations, they include factoring out the GCF and simplifying the factored equation. Another method is to use a trigonometric identity to reduce and then simplify the given eq

From playlist Solve Trigonometric Equations by Factoring

Video thumbnail

Introduction to number theory lecture 35 Jacobi symbol

This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We define the Jacobi symbol and prove its basic properties, and show how to calculate it fa

From playlist Introduction to number theory (Berkeley Math 115)

Related pages

Chebyshev pseudospectral method | Legendre polynomials | PROPT | Covector mapping principle | Ross–Fahroo lemma | DIDO (software) | Optimal control | Ross–Fahroo pseudospectral method | GPOPS-II | Pseudospectral optimal control