Nonlinear model predictive control with explicit back-offs for Gaussian process state space models

Nonlinear model predictive control (NMPC) is an efficient control approach for multivariate nonlinear dynamic systems with process constraints. NMPC does however require a plant model to be available. A powerful tool to identify such a model is given by Gaussian process (GP) regression. Due to data sparsity this model may have considerable uncertainty though, which can lead to worse control performance and constraint violations. A major advantage of GPs in this context is its probabilistic nature, which allows to account for plant-model mismatch. In this paper we propose to sample possible plant models according to the GP and calculate explicit back-offs for constraint tightening using closed-loop simulations offline. These then in turn guarantee satisfaction of chance constraints online despite the uncertainty present. Important advantages of the proposed method over existing approaches include the cheap online computational time and the consideration of closed-loop behaviour to prevent open-loop growth of uncertainties. In addition we show how the method can account for updating the GP plant model using available online measurements. The proposed algorithm is illustrated on a batch reactor case study.