yangwangaaa / Gaussian-Process-based-Model-Predictive-Control

Project for the course "Statistical Learning and Stochastic Control" at University of Stuttgart

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 and Report.

Supported Matlab Version >= R2019a

Control of a Race Vehicle with unkown complex dynamics

To run the Race Car example execute:

main_singletrack.m

A Gaussian process is used to learn unmodeled dynamics

$$x_{k+1} = f_d(x_k,u_k) + B_d * ( GP(z_k) + w ) , where z_k = [Bz_x*xk ; Bz_u*uk] is the vector of selected features f_d is the dicrete nominal model w ~ N(0,\sigma_n) is the process WG noise GP is the Gaussian Process model reponsible for learning the unmodeled dynamics$$

The Gaussian Process model GP is then fed with data (X,Y+w) collected online, such that:

$$X = [x_k,u_k] Y + w = pinv(B_d) * ( x_{k+1} - f_d(x_k,u_k) )$$

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	Adaptive NMPC controller (with trained Gaussian Process)

Control of an Inverted Pendulum with deffect motor

To run the Inverted Pendulum please execute

main_invertedPendulum.m