A simple and fast robust nonlinear model predictive control heuristic using n-steps-ahead uncertainty predictions for back-off calculations

A new robust nonlinear model predictive control (RNMPC) heuristic is proposed, specifically developed to be i) easy to implement, ii) robust against constraint violations and iii) fast to solve. Our proposed heuristic samples from the disturbance distributions and performs $n$-steps-ahead Monte Carlo (MC) simulations to calculate the back-off where $n$ is a small number, typically one. We show two implementations of our heuristic. The Automatic Back-off Calculation NMPC (ABC-NMPC) uses MC simulations on a process model to calculate the back-off, and explicitly states the back-off in a standard NMPC problem. Our second implementation, the MC Single-Stage NMPC (MCSS-NMPC), directly includes the disturbance distribution in the optimization problem, making it an implicit back-off method. Our methods are robust against constraint violation in the next time-step, under certain assumptions. In the presented case-study, our proposed RNMPC methods outperform the popular multi-stage NMPC in terms of robustness and/or computational cost. We suggest several further modifications to our RNMPC methods to improve performance, at the cost of increased complexity.