# Gaussian-Process-based-Model-Predictive-Control

**Repository Path**: jia-chunchun/Gaussian-Process-based-Model-Predictive-Control

## Basic Information

- **Project Name**: Gaussian-Process-based-Model-Predictive-Control
- **Description**: Project for the course "Statistical Learning and Stochastic Control" at University of Stuttgart
- **Primary Language**: Unknown
- **License**: Not specified
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
- **Forks**: 0
- **Created**: 2021-04-26
- **Last Updated**: 2021-04-26

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

# Gaussian-Process based Model Predictive Control [IN PROGRESS]
Project for the course "Statistical Learning and Stochastic Control" at University of Stuttgart


For detailed information about the project, please refer to the [Presentation](./Presentation.pdf) and [Report](./Report.pdf).

Supported Matlab Version **>= R2019a**


## Control of a Race Vehicle with unkown complex dynamics

To run the Race Car example execute:
> main_singletrack.m

<br>

A Gaussian process is used to learn unmodeled dynamics
```math
    x_{k+1} = f_d(x_k,u_k) + B_d * ( GP(z_k) + w )

    , where z_k = [Bz_x*xk ; Bz_u*uk] is the vector of selected features
            f_d is the dicrete nominal model
            w ~ N(0,\sigma_n) is the process WG noise
            GP is the Gaussian Process model reponsible for learning the unmodeled dynamics

```
The Gaussian Process model GP is then fed with data (X,Y+w) collected online, such that:
```math
    X = [x_k,u_k]
    Y + w = pinv(B_d) * ( x_{k+1} - f_d(x_k,u_k) )
```
and it is trained (hyperparameter optimization) by maximizing the log Likelihood p(Y|X,theta), where theta is the vector of hyperparameters.



### Results


| NMPC controller with unmodelled dynamics        | Learning-Based NMPC controller (with trained Gaussian Process)         |
| ------------- |-------------|
| <img src="./simresults/trackAnimVideo-16-Jan-2020-without-GP.gif" alt="drawing" width="400"/>      | <img src="./simresults/trackAnimVideo-16-Jan-2020-with-GP-optimized.gif" alt="drawing" width="400"/>    |

<br>

## Control of an Inverted Pendulum with deffect motor

To run the Inverted Pendulum please execute
> main_invertedPendulum.m