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Newton method of Nonlinear Model Predictive Control

This program is about NMPC with newton method. Usually we have to calculate the partial differential of optimal matrix. In this program, in stead of using any paticular methods to calculate the partial differential of optimal matrix, I used numerical differentiation. Therefore, I believe that it easy to understand and extend your model.

Problem Formulation

example
model

$\begin{bmatrix} \dot{x_1} \\ \dot{x_2} \\ \end{bmatrix} = \begin{bmatrix} x_2 \\ (1-x_1^2-x_2^2)x_2-x_1+u \\ \end{bmatrix}, |u| \leq 0.5$

evaluation function

To consider the constraints of input u, I introduced dummy input.

$J = \frac{1}{2}(x_1^2(t+T)+x_2^2(t+T))+\int_{t}^{t+T}\frac{1}{2}(x_1^2+x_2^2+u^2)-0.01vd\tau$

two wheeled model

coming soon !

Expected Results

example

![Figure_1.png](https://github.com/Shunichi09/linear_nonlinear_control/blob/demo_gif/nmpc/newton/Figure_1.png width = 70%)

you can confirm that the my method could consider the constraints of input.

two wheeled model

coming soon !

Usage

for example

$ python main_example.py

for two wheeled

coming soon !

Requirement

python3.5 or more
numpy
matplotlib

Reference

I`m sorry that main references are written in Japanese

main (commentary article) (Japanse)　https://qiita.com/MENDY/items/4108190a579395053924
Ohtsuka, T., & Fujii, H. A. (1997). Real-time Optimization Algorithm for Nonlinear Receding-horizon Control. Automatica, 33(6), 1147–1154. https://doi.org/10.1016/S0005-1098(97)00005-8
非線形最適制御入門（コロナ社）
実時間最適化による制御の実応用（コロナ社）

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Newton method of Nonlinear Model Predictive Control

Problem Formulation

Expected Results

Usage

Requirement

Reference

2.6 KiB

Raw Blame History