GitHub

Nonlinear Model-Predictive Control Using Koopman Operator

This document provides a detailed explanation of the MATLAB code that demonstrates the application of the Koopman operator theory for controlling a nonlinear system using Model Predictive Control (MPC ...
IEEE

Computing Input-Ouput Properties of Coupled Linear PDE systems

Abstract: In this paper, we propose an LMI-based approach to analyze input-output properties of coupled linear PDE systems. This work expands on a newly developed state-space theory for coupled PDEs ...
Scientific Research Publishing

Pazy, A. (1983) Semigroups of Linear Operators and Applications to PDE. Springer.

ABSTRACT: This paper is concerned with a modified transitional Korteweg-de Vries equation u t +f( t ) u 2 u x + u xxx =0 , ( x,t )∈ R + × R + with initial value u( x,0 )=g( x )∈ H 4 ( R + ) and ...
marktechpost

Newton Informed Neural Operator: A Novel Machine Learning Approach for Computing Multiple Solutions of Nonlinear Partials Differential Equations

Neural networks have been widely used to solve partial differential equations (PDEs) in different fields, such as biology, physics, and materials science. Although current research focuses on PDEs ...
marktechpost

This Paper Unravels the Mysteries of Operator Learning: A Comprehensive Mathematical Guide to Mastering Dynamical Systems and PDEs (Partial Differential Equation) through ...

The remarkable potentials of Artificial Intelligence (AI) and Deep Learning have paved the way for a variety of fields ranging from computer vision and language modeling to healthcare, biology, and ...
The Conversation

Has a mathematician solved the ‘invariant subspace problem’? And what does that even mean?

Nathan Brownlowe does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond ...
GitHub

@linear-gradient macro broken in ternary operator #1235

a:compilerSlint compiler internal (not the codegen, not the parser)Slint compiler internal (not the codegen, not the parser) When using the @linear-gradient macro in the 2nd position of the ternary ...
Scientific Research Publishing

A. Pazy, “Semigroup of Linear Operators and Applications to Partial Differential Equations,” Springer-Verlag, Berlin, 1983.

ABSTRACT: An elastic beam system formulated by partial differential equations with initial and boundary conditions is investigated in this paper. An evolution equation corresponding with the beam ...
IEEE

Parametrization for control of linear PDE systems

Abstract: Pseudo-differential operators (/spl psi/DO) form an extension of combined partial differential equations (PDE) and boundary-value (trace) operators. Applicability of /spl psi/DOs lies in the ...