Risk Averse Model Predictive Control of Bioreactors

Abstract

Uncertainty is inherent in bioprocess modelling and control. Typically, uncertainties are handled using either the stochastic approach or the robust approach. Recently, the risk-averse approach, i.e., an interpolation between the stochastic and worst-case robust approach is gaining popularity. Risk-averse formulations are very useful in avoiding conservative solutions while still handling high-effect, low-probability events. In the bioreactor case considered in this paper, one such high effect low probability event is wash off caused by high feed rate or low inlet substrate concentration. A risk-averse, risk-constrained model predictive control formulation is proposed in this paper. The dynamic optimisation problem to be solved at every measurement instance is formulated using AV@R type risk objective. Similarly, probabilistic chance constraints are approximated by an AV@R-type risk constraints. The problem is then solved using the conic duality of the risk measure and an epigraphical decomposition of the nested multistage problem.