Real-time optimization under parametric uncertainty: a probability constrained approach

Abstract Uncertainty is an inherent characteristic in most industrial processes, and a variety of approaches including sensitivity analysis, robust optimization and stochastic programming have been proposed to deal with such uncertainty. Uncertainty in a steady state nonlinear real-time optimization (RTO) system and particularly making robust decisions under uncertainty in real-time has received little attention. This paper discusses various sources of uncertainty within such closed loop RTO systems and a method, based on stochastic programming, that explicitly incorporates uncertainty into the RTO problem is presented. The proposed method is limited to situations where uncertain parameters enter the constraints nonlinearly and uncertain economics enter the objective function linearly. Our approach is shown to significantly improve the probability of a feasible solution in comparison to more conventional RTO techniques. A gasoline blending example is used to demonstrate the proposed robust RTO approach.