Sensitivity-Assisted multistage nonlinear model predictive control: Robustness, stability and computational efficiency

Abstract

Key requirements for robust nonlinear model predictive control (NMPC) are stability, efficient performance under uncertainty, constraint satisfaction and computational efficiency. Multistage NMPC, based on a scenario tree formulation for the uncertainty, has been shown to satisfy the first three objectives under plant-model mismatch. However, a limiting factor in multistage NMPC, is the exponential scaling of the scenarios with respect to uncertain parameters and the length of the robust horizon. To address this issue, we present an approximate sensitivity-assisted multistage NMPC (samNMPC) scheme that reduces the problem size by dividing the scenario set into critical and noncritical scenarios, with the former composed of the worst-case realizations of the uncertain parameters. In this approach, the optimization is sought explicitly over the critical scenarios, while noncritical scenarios are included implicitly through nonlinear programming (NLP) sensitivity-based approximations in the objective function. A key advantage of the proposed approach is that the problem size is independent of the number of constraints and scales only linearly with the robust horizon. This allows faster computations with longer robust horizons that rigorously account for future uncertainty. In this paper, we explore the samNMPC approach and discuss its robust stability properties in context of the robust horizon. We demonstrate the applicability of the approach for the continuous stirred tank reactor (CSTR) and the quadtank case studies for tracking setpoints, and show that samNMPC compares favorably in performance and robustness to ideal multistage NMPC, but with a significant reduction in computational cost.