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

$$x_{k+1}=f_d(x_k,u_k)+B_d\ast (GP(z_k)+w),where{z}_k=[B{z}_x\ast xk;B{z}_u\ast uk]isthevectorofselectedfeatures{f}_{d}isthedicretenominalmodelwN(0,{\sigma }_n)istheprocessWGnoiseGPistheGaussianProcessmodelreponsibleforlearningtheunmodeleddynamics$$

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

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

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