Welcome to the repository for Pseudospectral Methods in Optimal Control. This repository contains my work and studies throughout my course on Pseudospectral Methods, focusing on topics ranging from interpolation to spectral methods and their application in optimal control.
The repository is organized into the following key topics, each with theoretical explanations, code examples, and related plots:
- Optimal Control: Methods for solving optimal control problems, including direct and indirect methods, and static Lagrange multipliers.
- Interpolation: Understanding interpolation methods, including Lagrange interpolation, Newton's divided difference, and Barycentric interpolation.
- Orthogonal Polynomials: Exploring the recurrence relations of Legendre, Chebyshev, and other orthogonal polynomials.
- Spectral Methods: A deep dive into Fourier series, Galerkin methods, and the application of spectral methods for solving boundary value problems.
- Galerkin Method: Deriving and analyzing the error terms when applying Galerkin methods.
- Gauss-Jacobi Integration: Numerical integration using Gaussian quadrature and Chebyshev nodes.
- Bernstein Polynomials: Studying the Bernstein polynomials and their role in uniform approximation.
- Fourier Approximation