Stochastic Optimal Control in Batch Reactive Systems:Developments on Engineering Applications of Real Option Theory

摘要

This work focuses on optimal control problems and on the development of an integrated approach based on real option theory and sampling for addressing uncertainties in a systematic way.Our approach considers the general case of having model based uncertainties as well as external uncertainties.Time-dependent uncertainties in model parameters are modeled as Ito processes;external uncertainties are represented through continuous probability distributions,so that a sampling technique is used to generate the realizations of such variables before operation.Also,we have extended the existing theory for stochastic optimal control to include cases with path constraints on state variables in the problem formulation.Furthermore,our integrated approach for solving optimal control problems in the presence of uncertainties considers both theoretical and numerical methods,such as the stochastic maximum principle and the stochastic dynamic programming technique(for singular problems).We use the optimization of batch reactive systems under uncertainty as our case study to validate the theory and methods.Results show the effects of uncertainties on the operation profiles.