MPC with Gaussian Processes
Gaussian process (GP) regression has been widely used in supervised machine learning for its flexibility and inherent ability to describe uncertainty in the prediction. In the context of control, it is seeing increasing use for modeling of nonlinear dynamical systems from data, as it allows for direct assessment of the residual model uncertainty.
In practice, a nominal linear model is often available, while more complex nonlinearities can be challenging and time-intensive to model from first principles. We develop a model predictive control (MPC) approach that integrates a nominal linear system with an additive nonlinear part of the dynamics modeled as a GP. The resulting nonlinear stochastic control problem specifically takes into account the model uncertainties associated with the GP, and thus enables cautious control of the system.
Lukas Hewing and Melanie N. Zeilinger. Predictive Control with Model Uncertainty Estimation using Gaussian Process Regression. 4th European Conference on Computational Optimization, Leuven, 2016.
[abstract] (PDF, 63 KB)