Gaussian Process based Model Predictive Control for Linear Time Varying systems

Two main issues associated with Model Predictive Control (MPC) are learning the unknown dynamics of the system and handling model uncertainties. In this paper, unknown Linear Time-Varying (LTV) system with external noise is represented by using probabilistic Gaussian Process (GP) models. In this way, we can explicitly evaluate model uncertainties as variances. As a result, it is possible to directly take obtained variances into account when planing the policy. In addition, through using analytical gradients that are available during the GP modelling process, the optimization problem in GP based MPC can be solved faster. The performance of proposed approach is demonstrated by simulations on trajectory tracking problem of a LTV system.