Sensitivity-assisted Robust Nonlinear Model Predictive Control with Scenario Generation

Abstract

We propose a sensitivity-assisted multistage Nonlinear Model Predictive Control strategy, called samNMPC, to address multistage stochastic programs for robust NMPC. Our approach divides the scenario sets in the stochastic programming formulation into critical and noncritical sets. Critical scenarios are selected by scenario generation based on worst-case constraint determination, while stage costs for noncritical scenarios are determined by sensitivity-based approximations. The resulting multi-stage NMPC problem leads to a first order accurate control profile that satisfies all constraints under uncertainty. Moreover, computational costs of this formulation scale independently of the number of disturbance variables, and only linearly with the robust horizon and number of constraints. Our proposed approach is illustrated on a CSTR (continuous stirred tank reactor) case study with two uncertain parameters. Compared to competing approaches, samNMPC delivers robust performance of multi-stage NMPC with significantly less computational cost.