(380c) Process Design with Robust Stability Under Parametric Uncertainty
Process design for steady state operation requires identification of a most profitable point of operation. Since the mathematical representation of the underlying physical process has modeling errors, the calculated design point is not guaranteed to be the real operating point. Moreover, disturbances can force the process away from the desired stationary point. Therefore, design techniques must also address the minimization of modeling and operational uncertainties at the design stage. Naturally, stability and stabilizability are dynamic properties that become inportant in this context.
Stability analysis is closely tied with finding the most positive real part of eigenvalues of a real matrix. When this objective is coupled with an economic design objective, process design problems result into difficult bilevel optimization problems. Using classical Routh-Hurwiz stability criteria, we have recently developed an equivalent single-level mathematical programming formulation . For the case of robust stability, i.e., when stability required over a range of parameters, this approach results in a challenging nonconvex semi-infinite problem, which is addressed in this work.
In order to solve the semi-infinite program to global optimality, we developed a successive column and row generation algorithm. Our algorithm can be also applied to a class of generalized semi-infinite programs with equilibrium constraints. The proposed formulation and solution algorithm were applied to chemical and biochemical process design problems, with and without control, and identified globally optimal designs satisfying the robust stability conditions. The proposed methodology and extensive computational results will be presented.
 Y. Chang and N. V. Sahinidis, "Optimization of metabolic pathways under stability considerations," Comp. Chem. Eng. 29:467-479, 2005.