Cautious Model Predictive Control using Gaussian Process Regression

Gaussian process (GP) regression has been widely used in supervised machine learning for its flexibility and inherent ability to describe uncertainty in the function estimation. In the context of control, it is seeing increasing use for modeling of nonlinear dynamical systems from data, as it allows the direct assessment of residual model uncertainty. We present a model predictive control (MPC) approach that integrates a nominal linear system with an additive nonlinear part of the dynamics modeled as a GP. Approximation techniques for propagating the state distribution are reviewed and the benefits of considering feedback in the prediction is demonstrated. We describe a principled way of formulating the chance constrained MPC problem, which takes into account residual uncertainties provided by the GP model to enable cautious control. Efficient computation with state-of-the-art solvers is discussed and simulation examples demonstrate the feasibility of the approach for systems with subsecond sampling times.