Gaussian Process Based Stochastic Model Predictive Control of Linear System with Bounded Additive Uncertainty

This paper presents a Gaussian process based stochastic model predictive control method for linear time-invariant systems subject to bounded state-dependent additive uncertainties. Chance constraints are treated in analogy to tube-based MPC. To reduce the conservatism, the adaptive constraint tightening is performed by using the confidence region of the predicted uncertainty which is formulated based on the output of the Gaussian process model. Numerical simulations demonstrate the conservatism reducing advantage of the proposed Gaussian process based stochastic model predictive control algorithm in comparison with existing methods.