Abstract
Nonlinear model predictive control (NMPC) is one of the few methods that can handle multivariate nonlinear control problems while accounting for process constraints. Many dynamic models are however affected by significant stochastic uncertainties that can lead to closed-loop performance problems and infeasibility issues. In this paper we propose a novel stochastic NMPC (SNMPC) algorithm to optimize a probabilistic objective while adhering chance constraints for feasibility in which only noisy measurements are observed at each sampling time. The system predictions are assumed to be both affected by parametric and additive stochastic uncertainties. In particular, we use polynomial chaos expansions (PCE) to expand the random variables of the uncertainties. These are updated using a PCE nonlinear state estimator and exploited in the SNMPC formulation. The SNMPC scheme was verified on a complex polymerization semi-batch reactor case study.
Highlights
Batch processes play a vital role for the manufacture of high value products in many sectors of the chemical industry, such as pharmaceuticals, polymers, biotechnology, and food
Model predictive control (MPC) is an advanced control method that has been employed to a significant extent in industry due to its ability to deal with multivariate plants and process constraints
If we assume the uncertainties to lie in a bounded set, robust MPC (RMPC) methods are available to deal with this problem [3]
Summary
Batch processes play a vital role for the manufacture of high value products in many sectors of the chemical industry, such as pharmaceuticals, polymers, biotechnology, and food. The unscented transformation work in [11] assumes feedback from the Unscented Kalman filter, in [21] a probabilistic high-gain observer is proposed to be jointly used with a continuous-time SNMPC formulation and lastly [19] use the particle filter equations for both state estimation and uncertainty propagation. In the previous work additive process noise was ignored due to the issue time-varying uncertainties cause for PCE based methods. To address these issues we extended the approach in [30] to be able to handle additive disturbance noise and in addition formulate an efficient SNMPC algorithm using a sparse Gauss-Hermite (sGH) sampling rule.
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