多阶段伪谱法的基本实现

## README (basic-multiple-interval-pseudospectral) [](https://github.com/danielrherber/basic-multiple-interval-pseudospectral/releases/latest) [](https://www.mathworks.com/products/matlab.html) [](https://github.com/danielrherber/basic-multiple-interval-pseudospectral/issues) [](https://github.com/danielrherber/basic-multiple-interval-pseudospectral/graphs/contributors) [](https://github.com/danielrherber/basic-multiple-interval-pseudospectral/blob/master/License) This project implements multiple-interval pseudospectral methods to solve optimal control problems.  --- ### Install - Download the [project files](https://github.com/danielrherber/basic-multiple-interval-pseudospectral/archive/master.zip) - Run [INSTALL_Basic_Pseudospectral.m](https://github.com/danielrherber/basic-multiple-interval-pseudospectral/blob/master/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)* ```matlab INSTALL_Basic_Pseudospectral ``` - See [BD_main.m](https://github.com/danielrherber/basic-multiple-interval-pseudospectral/blob/master/examples/bryson-denham/BD_main.m) to run the Bryson-Denham example ```matlab open BD_main ``` - See the technical report [[PDF]](http://systemdesign.illinois.edu/publications/Her15a.pdf) for the theory and case study results ### Citation 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]](http://systemdesign.illinois.edu/publications/Her15a.pdf) ### Description 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). ### External Includes See [INSTALL_Basic_Pseudospectral.m](https://github.com/danielrherber/basic-multiple-interval-pseudospectral/blob/master/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]](https://people.maths.ox.ac.uk/trefethen/spectral.html) - Code from J. Shen, T. Tang, and L. Wang. **Spectral Methods: Algorithms, Analysis and Applications**, Springer, 2011. [[URL]](http://www.ntu.edu.sg/home/lilian/book.htm) --- ### General Information #### Contributors - [Daniel R. Herber](https://github.com/danielrherber) #### Project Links - [https://github.com/danielrherber/basic-multiple-interval-pseudospectral](https://github.com/danielrherber/basic-multiple-interval-pseudospectral) - [http://www.mathworks.com/matlabcentral/fileexchange/51104](http://www.mathworks.com/matlabcentral/fileexchange/51104)