It has long been recognized that the models used in chemical process design, control and optimization are typically subject to significant amounts of uncertainty. A traditional example is the continuous stirred-tank reactor (CSTR). In addition to the idealization involved in classifying a process vessel as a CSTR, the chemistry of the particular process is often simplified, or at least some of the reaction rate constants are not precisely known. More dramatically, the feed stream's flow rate, composition, or temperature may vary quite widely depending on upstream processes. This situation is only amplified when we start to consider the emerging fields of bioreactors and systems biology, where measurements are more expensive and the chemistry is more complex. Significant amounts of uncertainty are also introduced when we begin to consider larger questions like how to design an entire chemical plant for profitable operation over the next twenty years or what regulations should be imposed in order to ensure future atmospheric health.

Furthermore, while techniques based on linear models have had a lot of success in industry, current trends point to a need for techniques based on nonlinear models. For example, polymerization, crystallization and biological systems often exhibit significant nonlinearities. While it is sometimes possible to get acceptable performance from such systems using linear techniques, significant improvements are often realized when nonlinearities are taken into account. Another industrial trend is toward batch production of specialty chemicals. No matter whether this is done traditionally or biologically, the dynamic nature of batch processes often serves to highlight system nonlinearities, which should be accounted for in order to optimize performance. Since many design, control and optimization techniques are based on mathematical programming, these considerations have led me to focus on uncertain nonlinear programming formulations, algorithms and theory, and their application to problems like those mentioned above. In particular, two deterministic methodologies, parametric nonlinear programming (pNLP) and robust nonlinear programming (robust NLP), are considered.

This poster presents the parametric and robust nonlinear programming formulations, outlines recent contributions in these two fields and discusses applications. Specific components include an update on POPAK, a software package for parametric nonlinear programming; a description of potential application areas for pNLP; the presentation of a first-order robust NLP formulation along with a description of appropriate applications; and results for three example problems. pNLP and robust NLP both deal with nonlinear programs that contain uncertain parameters. The primary difference between these approaches is that pNLP seeks to determine the optimum for the NLP as a function of the uncertain parameters while robust NLP seeks a single optimum that is the best choice among all the points that would be feasible for all possible model realizations.