Chance constrained optimization of process systems under uncertainty: I. Strict monotonicity

An approach for chance constrained programming of large-scale nonlinear dynamic systems is presented. The stochastic property of the uncertainties is explicitly considered in the problem formulation in which some input and state constraints are to be complied with predefined probability levels. The method considers a nonlinear relation between the uncertain input and the constrained variables. It also involves efficient algorithms so as to compute the probabilities and, simultaneously, the gradients through integration by collocation in finite elements. The formulation of single or joint probability limits incorporates the issue of feasibility and the contemplation of trade-off between robustness and profitability regarding the objective function values. The approach is relevant to all cases when uncertainty can be described by any kind of joint correlated multivariate distribution function. Thus, chance constrained programming is a promising technique in solving optimization problems under uncertainty in system engineering. The potential and the efficiency of the presented systematic methodology, which assumes a strict monotonic relationship between the uncertain input and the uncertain constrained output, are illustrated with application to a reactive batch distillation processes under uncertainty.