Stochastic Nonlinear Model Predictive Control Using Gaussian Processes

Model predictive control is a popular control approach for multivariable systems with important process constraints. The presence of significant stochastic uncertainties can however lead to closed-loop performance and infeasibility issues. A remedy is given by stochastic model predictive control, which exploits the probability distributions of the uncertainties to formulate probabilistic constraints and objectives. For nonlinear systems the difficulty of propagating stochastic uncertainties is a major obstacle for online implementations. In this paper we propose to use Gaussian processes to obtain a tractable framework for handling nonlinear optimal control problems with Gaussian parametric uncertainties. It is shown how this technique can be used to formulate nonlinear chance constraints. The method is verified by showing the ability of the Gaussian process to accurately approximate the probability density function of the underlying system and by the closed-loop behaviour of the algorithm via Monte Carlo simulations on an economic batch reactor case study.