Online Learning Stochastic Model Predictive Control of Linear Uncertain Systems

This article presents an online learning stochastic model predictive control method for linear uncertain systems with state-dependent additive uncertainties, where the uncertainty is modeled as Gaussian process. The proposed scheme utilizes the probabilistic reachable sets as time-varying tubes, which are formulated by forecasting the variance propagation of uncertainty via Gaussian process regression, to embody the chance constraints. The proposed learning based stochastic model predictive control algorithm is designed by refining the active data dictionary to train the Gaussian process model of uncertainty online. In particular, the data points in the active data dictionary are selected from the raw data around the predicted optimal nominal trajectories, which reduces the computational load as well as preserves the control performance. Then the algorithm feasibility and closed-loop stability of the developed algorithm are analyzed. Finally, the efficacy and superiority over existing methods are verified by simulation studies.