Design of process operations using hybrid dynamic optimization

Accurate nonlinear dynamic models of process operations such as start-ups, shut-downs, and complex changeovers include state dependent events that trigger discrete changes to the describing equations, and are best analyzed within a hybrid systems framework. The automated design of an optimal process operation can thus be formulated as a dynamic optimization problem with a hybrid system embedded. However, the resulting optimization problems are often nonsmooth and nonconvex. Similarly, formal verification problems in the design of logic based controllers for abnormal situation management can often be formulated as optimization problems with hybrid systems embedded. However, for safety verification purposes, it is essential to guarantee that the global solution has been found. These applications motivate the development of deterministic global optimization algorithms for nonconvex, nonsmooth dynamic optimization problems with nonlinear hybrid systems embedded. This paper describes recent progress on the development of suitable algorithms. A method for constructing convex relaxations of general nonconvex NLP problems with linear dynamic systems embedded is presented. These convex relaxations are then extended to multistage problems with model switches between the stages. Finally, integer variables are introduced to represent alternative sequences of model switches. The ability to construct convex relaxations enables existing nonconvex MINLP algorithms to be applied to find the global solution of the resulting MIDO problems.