Efficient robust nonlinear model predictive control via approximate multi-stage programming: A neural networks based approach

Abstract Multi-stage nonlinear model predictive control (msNMPC) is a robust control strategy based on the description of the uncertainty propagation through a dynamic system via a scenario tree and is one of the least conservative approaches to robust control. The computational complexity of the msNMPC, however, grows with respect to the number of uncertainties and with respect to the length of the prediction horizon. This paper presents a new approach, where the optimal cost-to-go function is approximated after a specific point in time, here in particular by neural networks, so the independent branches do not have to be optimized but are approximated. The optimization might be casted over the robust horizon only, which reduces the computational burden, but still guarantees robust satisfaction of the constraints. Moreover, this approach allows to consider any length of the prediction horizon for the same computational cost. The neural network models are trained offline using the optimal profiles in all branches of the scenario tree. The potential of the proposed approach is demonstrated by simulation studies on a semi-batch reactor.