(705c) Robust Nonlinear Model Predictive Control with Scenario Reduction

Model Predictive Control (MPC) has been very successful in the past decades in process industries, especially with multiple input multiple output (MIMO) and constraint handling. Its nonlinear counterpart, nonlinear MPC, has been gaining more attentions recently due to its capacity in model accuracy for a wide range of states. However, for a dynamic system where nontrivial plant-model mismatch occurs, robust NMPC strategies need to be applied in order to ensure robust constraint satisfaction and optimal control performance under uncertainty.

In the past, [1] has shown that multistage NMPC is a promising robust NMPC scheme that builds a scenario tree to represent the uncertainty evolution. Due to its multi-model nature, the optimization problem that needs to be solved online grows exponentially as the number of uncertainty parameters and length of robust horizon increases. To manage the problem size, advanced-step multistage NMPC [2] has been introduced to separate the whole problem into background computations and online updates. Alternatively, [3] adaptively generates the scenario tree online for a semi-batch polymerization process.

Based on the multistage scenario tree, in this work, we consider an approximate multistage NMPC framework that contains only the nominal scenario and critical scenarios, where each critical scenario is defined as the worst-case scenario for a specific constraint. The goal is to reduce the number of scenarios contained in the optimization problem while approximating the rest of possible scenarios in the objective using sensitivity information. The scenario reduction framework is illustrated on a CSTR case study, and its performance is comparable with current state-of-the-art robust NMPC with far less computational workload.

References

[1] Lucia, S., Finkler, T., & Engell, S. (2013). Multi-stage nonlinear model predictive control applied to a semi-batch polymerization reactor under uncertainty. Journal of Process Control, 23(9), 1306-1319.

[2] Yu, Z. J., & Biegler, L. T. (2018). Advanced-step Multistage Nonlinear Model Predictive Control. IFAC-PapersOnLine, 51(20), 122-127.

[3] Holtorf, F., Mitsos, A., & Biegler, L. T. (2019). Multistage NMPC with on-line generated scenario trees: Application to a semi-batch polymerization process. Journal of Process Control, Submitted for publication.