Hybrid shooting - a new optimization method for unstable dynamical systems

Chemical processes are modeled by large-scale, highly-nonlinear process models often governed by unstable dynamics. Dynamic optimization is required to exploit economical performance of these processes in their unstable regions. On the one hand, direct single shooting is able to solve large-scale dynamic optimization problems, but lacks the ability to cope properly with unstable dynamical systems. On the other hand, the multiple shooting method is capable of dealing with instabilities but results in larger optimization problems. This work deals with a novel parameterization approach, termed hybrid shooting, which combines the advantages of single and multiple shooting into one approach. Similar to multiple shooting, stages are introduced and states with unstable properties are parameterized by free initial values at the beginning of each stage. This approach significantly enhances the behavior of the optimization problem by improving the condition of the underlying initial value problem (IVP).