Control and Uncertainty Propagation in the Presence of Outliers by Utilizing Student-t Process Regression

Gaussian Process Regression (GPR) has been extensively used to estimate unknown models and quantify model uncertainty in control tasks concerning safety-critical applications. However, one of the drawbacks of GPR is that it does not take into account the function evaluations of the observations in the uncertainty estimation, rendering it unsuitable for applications with observations prone to outliers or to some unassumed noise disturbance. In this work, we introduce the Student-t Process Regression (TPR) as a generalization of GPR for estimating dynamics models in the control literature. The key attribute of TPR is that the estimation variance explicitly depends on the function evaluations rendering it more robust to outliers. We prove uniform error bounds for the estimation based on TPR under certain continuity assumptions. Furthermore, we employ TPR to estimate unknown and nonlinear dynamical systems and we show with control simulations that the resulting estimation uncertainty compensates for the existence of outliers. Such informative variance estimates are of vital importance as they can lead to more informative uncertainty propagation and thus less conservative control policies.