Introduction

This project provides the continuation/GMRES method (C/GMRES method) based solvers for nonlinear model predictive control (NMPC) and an automatic code generator for NMPC, called AutoGenU.

The following C/GMRES based solvers are provided:

• The original C/GMRES method (single shooting)
• The multiple shooting based C/GMRES method
• The multiple shooting based C/GMRES method with condensing of variables with respect to the constraints on the saturation function on the control input

Requirement

• C++11 (MinGW and PATH to it are required for Windows users)
• CMake
• Python 3, Jupyter Lab or Jupyter Notebook, SymPy (to generate nmpc_model.hpp, nmpc_model.cpp, main.cpp, and CMakeLists.txt by AutoGenU.ipynb)
• Python 3, NumPy, seaborn (to plot simulation data on AutoGenU.ipynb)

Usage

AutoGenU

AutoGenU.ipynb generates following source files under your setting state equation and cost function:

• nmpc_model.hpp
• nmpc_model.cpp
• main.cpp
• CMakeLists.txt

You can also build source files for numerical simulation, execute numerical simulation, and plot or save simulation result on AutoGenU.ipynb.

C/GMRES based solvers of NMPC

The C/GMRES based solvers in src/solver directory can be used independently of AutoGenU.ipynb. You are then required the following files:

• nmpc_model.hpp: write parameters in your model
• nmpc_model.cpp: write equations of your model
• main.cpp: write parameters of solvers

In addition to these files, you have to write CMakeLists.txt to build source files.

Demos

• Inverting a pendubot using the multiple shooting based C/GMRES method

• Inverting a pendubot using the multiple shooting based C/GMRES method with condensing of variables with respect to the constraints on the saturation function on the control input

License

MIT

References

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)