Tube‐based stochastic model predictive control leveraging Gaussian process regression for linear systems with bounded additive uncertainties

Abstract This paper presents an adaptive tube‐based stochastic model predictive control algorithm for linear systems with state‐dependent additive uncertainties. Specifically, the uncertainty of the system is modeled using Gaussian process regression, and the information predicted by Gaussian process regression online is leveraged to establish a confidence region for the uncertainty. By employing this confidence region, the time‐varying probabilistic reachable set, referred to as a tube, is computed. Subsequently, the Gaussian process‐based stochastic model predictive control algorithm is devised by employing the probabilistic reachable set to redefine the state constraint. Furthermore, the recursive feasibility of the algorithm and the stability of the closed‐loop system are proved. Finally, the effectiveness and superiority over existing methods are validated by numerical simulations.