This project provides Continuation/GMRES method (C/GMRES method), a fast algorithm of NMPC, and the multiple shooting based C/GMRES method.

• C++11
• Cmake
• Eigen 3
• Python3, numpy, seaborn (for plotsim.py and 2linkanimation.py)
• ffmpeg (to save animations generated by 2linkanimation.py)

mkdir -p ~/mayataka/cmgres && cd ~/mayataka/cmgres && git init
git remote add gh [email protected]:benjaminabruzzo/CGMRES.git && git pull gh master && git fetch gh

After setting the parameters of your model of NMPC in nmpc_model.hpp, writing equations in nmpc_model.cpp, and setting simulation conditions in main.cpp, build files as follows:

$ mkdir build
$ cd build
$ cmake ..
$ make

After performing a numerical simulation, you can see graphs by

$ python3 plotsim.py example

save graphs by

$ python3 plotsim.py example save example

see an animation of 2link robot by

$ python3 2linkanimation.py example

and save its animation by

$ python3 2linkanimation.py example save example

mkdir -p ~/mayataka/cmgres && cd ~/mayataka/cmgres && git init

1. T. Ohtsuka A continuation/GMRES method for fast computation of nonlinear receding horizon control, Automatica, Vol. 40, No. 4, pp. 563-574 (2004)
2. C. T. Kelly, Iterative methods for linear and nonlinear equations, Frontiers in Apllied Mathematics, SIAM (1995)
3. Y. Shimizu, T. Ohtsuka, M. Diehl, A real‐time algorithm for nonlinear receding horizon control using multiple shooting and continuation/Krylov method, International Journal of Robust and Nonlinear Control, Vol. 19, No. 8, pp. 919-936 (2008)