danielrherber / basic-multiple-interval-pseudospectral Goto Github PK

This project implements multiple-interval pseudospectral methods to solve optimal control problems.

• Download the project files
• Run INSTALL_Basic_Pseudospectral.m in the MATLAB Command Window (automatically adds project files to your MATLAB path, downloads the required files, and opens an example)

INSTALL_Basic_Pseudospectral

• See BD_main.m to run the Bryson-Denham example

open BD_main

• See the technical report [PDF] for the theory and case study results

The code is complementary material for the following publication:

• DR Herber. Basic Implementation of Multiple-Interval Pseudospectral Methods to Solve Optimal Control Problems. Technical report, Engineering System Design Lab, UIUC-ESDL-2015-01, Urbana, IL, USA, Jun 2015. [PDF]

The two numerical schemes are used: the Legendre pseudospectral method with LGL nodes and the Chebyshev pseudospectral method with CGL nodes. The results from the case studies using the Bryson-Denham problem demonstrate the effect of user's choice in mesh parameters and little difference between the two numerical pseudospectral schemes. The solution procedure is independent of Bryson-Denham problem the test so other optimal control problems can be solved with the accompanying code.

The main purpose of this submission is to provide a reference for the basic implementation of multiple-interval pseudospectral methods. Paired with the technical report of the same name, I hope to help bring this advanced method for solving optimal control problems to a broader audience (especially in the classroom).

See INSTALL_Basic_Pseudospectral.m for more information

• MATLAB File Exchange Submission IDs (23629, 40397)
• Code from Lloyd N. Trefethen. Spectral Methods in MATLAB, SIAM, 2000. [URL]
• Code from J. Shen, T. Tang, and L. Wang. Spectral Methods: Algorithms, Analysis and Applications, Springer, 2011. [URL]

• Daniel R. Herber

• https://github.com/danielrherber/basic-multiple-interval-pseudospectral
• http://www.mathworks.com/matlabcentral/fileexchange/51104