Results 221 to 230 of about 516,382 (294)

Adaptive control of a class of uncertain nonlinear systems using brain emotional learning and Legendre polynomials

Transactions of the Institute of Measurement and Control, 2023
In this paper, an adaptive controller for a class of uncertain nonlinear systems is presented using a combination of Legendre polynomials and brain emotional learning-based intelligent controller (BELBIC).
Fatemeh Amiri, S. Khorashadizadeh
semanticscholar   +1 more source

Numerical analysis of nonlinear variable fractional viscoelastic arch based on shifted Legendre polynomials

Mathematical methods in the applied sciences, 2021
An innovative numerical procedure for solving the viscoelastic arch problem based on variable fractional rheological models, directly in time domain, is proposed and investigated.
Jiawei Cao, Yiming Chen, Yuanhui Wang, Hua Zhang   +3 more
semanticscholar   +1 more source

Recurrence Legendre Polynomials

Moscow University Mathematics Bulletin, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +2 more sources

Reverse Legendre polynomials

Archiv der Mathematik, 2022
Let \(\mathcal{P}\) be the vector space of all polynomials, equipped with the inner product \(\langle f(x), g(x)\rangle=\int_{-1}^{1} f(x) g(x) d x\). The Legendre polynomials \(P_{0}(x), P_{1}(x), \ldots\) are the polynomials obtained by applying the Gram-Schmidt procedure to the ordered basis \(\mathcal{B}=\left\{1, x, x^{2}, \ldots\right\}\) of ...
openaire   +2 more sources

Numerical solution of nonlinear fractal‐fractional optimal control problems by Legendre polynomials

Mathematical methods in the applied sciences, 2020
This article is devoted to developing an accurate operational matrix (OM) method for the solution of a new category of nonlinear optimal control problems (OCPs) explained by fractal‐fractional dynamical systems.
M. Heydari, A. Atangana, Z. Avazzadeh
semanticscholar   +1 more source

Numerical solution of multiterm variable‐order fractional differential equations via shifted Legendre polynomials

Mathematical methods in the applied sciences, 2019
In this paper, shifted Legendre polynomials will be used for constructing the numerical solution for a class of multiterm variable‐order fractional differential equations.
A. A. El-Sayed, P. Agarwal
semanticscholar   +1 more source

Direct adaptive model-free control of a class of uncertain nonlinear systems using Legendre polynomials

Transactions of the Institute of Measurement and Control, 2019
In this paper, a simple model-free controller for a class of uncertain nonlinear systems is presented using Legendre polynomials. According to the orthogonal functions theorem, Legendre polynomials are universal approximators.
Reza Zarei, S. Khorashadizadeh
semanticscholar   +1 more source

Numerical solution of the conformable differential equations via shifted Legendre polynomials

International Journal of Computational Mathematics, 2019
In this paper, we are concerned with the linear and nonlinear multi-term fractional differential equations. Firstly, a new approximate formula of the conformable fractional derivative is derived.
Handan Çerdik-Yaslan, Ferdi Mutlu
semanticscholar   +1 more source

Using orthogonal Legendre polynomials to parameterize global geophysical optimizations: Applications to seismic‐petrophysical inversion and 1D elastic full‐waveform inversion

Geophysical Prospecting, 2018
We use Legendre polynomials to reparameterize geophysical inversions solved through a particle swarm optimization. The subsurface model is expanded into series of Legendre polynomials that are used as basis functions.
M. Aleardi
semanticscholar   +1 more source

Structure preserving balanced proper orthogonal decomposition for second‐order form systems via shifted Legendre polynomials

IET Control Theory & Applications, 2019
This study considers structure preserving balanced proper orthogonal decomposition for second-order form systems via shifted Legendre polynomials. The proposed approach is to use time interval empirical Gramians of the first-order representation, which ...
Zhi-Hua Xiao, Yaolin Jiang, Zhen-Zhong Qi   +2 more
semanticscholar   +1 more source