README (optimal-control-direct-method-examples)
Teaching examples for three direct methods for solving optimal control problems, namely single shooting, single step, and pseudospectral.
Install
- Download the project files
- Run INSTALL_Direct_Method_Examples.m in the MATLAB Command Window (automatically adds project files to your MATLAB path, downloads the required files, and opens an example)
INSTALL_Direct_Method_Examples- See Run_All_Examples.m to run all the examples or the individual examples in
/src
Run_All_ExamplesExternal Includes
See INSTALL_Direct_Method_Examples.m for more information
- MATLAB File Exchange Submission IDs (51104, 65434)
MATLAB Version
The main methods should work on version R2014b or newer. Method_DTQPProject.m requires version R2016a or newer. Some of the plot decorations require newer versions that support structure properties in figures. The Optimization Toolbox is required.
Bryson-Denham Problem
This is the optimal control problem used in the examples. The problem formulation is:
The optimal control solution when \ell is between 0 and 1/6 is:
Please see the following files that calculate the optimal states and control. See pages 120–123 of A. E. Bryson and Y.-C. Ho, Applied Optimal Control, revised printing ed. Taylor & Francis, 1975 for more details on this problem.