Stochastic Nonlinear Model Predictive Control of an Uncertain Batch Polymerization Reactor

This paper presents a stochastic nonlinear model predictive control technique for discrete-time uncertain nonlinear systems with particular focus on the batch polymerization reactor application. We consider a nonlinear dynamical system subject to chance constraints (i.e. need to be satisfied probabilistically up to a pre-assigned level). This formulation leads to a finite-horizon chance-constrained optimization problem at each sampling time, which is in general non-convex and hard to solve. We propose a heuristic methodology to handle uncertainty for highly nonlinear systems. In our framework, the uncertainty propagation is modelled via a Markov chain and a randomization technique, the so-called scenario approach, is employed yielding a tractable formulation. The efficiency and limitations of the proposed methodology is illustrated through its application to an uncertain batch polymerization reactor model and a comparison with deterministic nonlinear model predictive control is presented.