Multi-Step Gaussian Regression Prediction in Dynamic Systems: A Case Study in Vehicle Lateral Control

Abstract

Abstract In this paper, we focus on developing a multi-step uncertainty propagation method for systems with state- and control-dependent uncertainties. System uncertainty creates a mismatch between the actual system and its control-oriented model. Often, these uncertainties are state- and control-dependent, such as modeling error. This uncertainty propagates over time and results in significant errors over a given time horizon, which can disrupt the operation of safety-critical systems. Stochastic predictive control methods can ensure that the system stays within the safe region with a given probability, but requires prediction of the future state distributions of the system over the horizon. Predicting the future state distribution of systems with state- and control-dependent uncertainty is a difficult task. Existing methods only focus on modeling the current or one-step uncertainty, while the uncertainty propagation model over a horizon is generally over-approximated. Hence, we present a multi-step Gaussian process regression method to learn the uncertainty propagation model for systems with state- and control-dependent uncertainties. We also perform a case study on vehicle lateral control problems, where we learn the vehicle’s error propagation model during lane changes. Simulation results show the efficacy of our proposed method.