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	Learning-Based NMPC controller (with trained Gaussian Process)

Control of an Inverted Pendulum with deffect motor

To run the Inverted Pendulum please execute

main_invertedPendulum.m