Deep-Neuro Control with Contraction Theory

Description

The objectives of this research are as follows:

• Mathematical stability analysis of the controller and estimator with deep neural networks using the contraction theory.
• Development of the controller and estimator with deep neural networks using the contraction theory.

Tables of Contents

You can find draft ./manuscript.pdf and ./doc/document.pdf.

├── README.md                   // you are here
├── manuscript.tex              // template of manuscript
├── dding_template              // pre-defined template
├── figures                     // general figures
├── public                      // do not touch
├── localRefs.bib               // bibtex file
├── docs                        // documentation
└── src                         // source code
    ├── script_simulation       // script sim. example
    │   ├── figures             //             figures
    │   └── results             //             results
    └── simulink_simulation     // simulink sim. example
        ├── figures             //               figures
        └── results             //               results

How to start

If you have questions, please, please, let the author knows.

Download this remote repository on your local device.

git clone https://gitlab.com/dding_friends/dding_research

Initialize submodule to download Template repository.

This command will download very recent version of Template

git submodule init
git submodule update

I provide you the keywords that you can google what you need for what you want to do.

Keywords	Descriptions
branch	Want to

Example research simulation and manuscript

This simulation in ./src provides simple feedback control example. Please, read src/script_simulation/main.m and src/simulink_simulation/main_slx.m for script and Simulink simulations, respectively. When you run those scripts, the results and figures shall be saved in the directories named results and figures (of course, you need to check setting in the scripts.).

Consider following control-affine system represented as $$ \dot {\boldsymbol{x}} = \boldsymbol{A}\boldsymbol{x} + \boldsymbol{B}\boldsymbol{u} $$ where $\boldsymbol{x}=[x_1;x_2]\in\mathbb{R}^2$ denotes state variables, $\boldsymbol{u}=[u_1;u_2]\in\mathbb{R}^2$ denotes control input variables, and $\boldsymbol{A}=[0,1;-2,-3]\in\mathbb{R}^{2\times2}$ and $\boldsymbol{B}=I_2\in\mathbb{R}^{2\times2}$ denote system and input matrices, respectively. The initial condition are $\boldsymbol x\vert_{t=0} = [0;0]^\top$ and $\boldsymbol u\vert_{t=0} = [0;0]^\top$.

Suppose that we have smooth reference trajectory of $\boldsymbol{x}$ as follows: $$ \boldsymbol{r} = \begin{bmatrix} r_1 \ r_2 \end{bmatrix} = \begin{bmatrix} \sin(t)\ \cos(t) \end{bmatrix} \in\mathbb{R}^2 $$ A feedback control law can be designed as follows: $$ \boldsymbol{u} = -\boldsymbol{K}\boldsymbol{e} $$ where $\boldsymbol{e}\triangleq \boldsymbol{x}-\boldsymbol{r}$ denotes tracking error and $\boldsymbol{K}=\text{diag}([-2,-3])\in\mathbb{R}^{2\times 2}$ denotes control gain matrix.

Then the simulation results are plotted like below.

Authors

• Ryu Myeongseok @DDingR
• You Sesun @yousesun95
• Choi Kyunhhwan

License