Progressor Transformation of Dynamical Systems and Application to Dynamic Optimization^*

Motivated by dynamic optimization of aluminium extrusion, this paper demonstrates how a progressor transformation of dynamical models can simplify the implementation of simultaneous methods for dynamic optimization. The implementation of direct collocation becomes difficult when the model exhibits known discontinuous changes, but at unknown times. If the model changes happen at known values in another progressor, the model can be transformed and implemented effortlessly. An example from the extrusion process is given, where the extrusion process model is transformed from time to extrusion length. The transformation allowed the implementation of direct collocation. In addition, the predictability of the transformed model allowed nearly a 50 percent reduction in state variables for describing the aluminium billet throughout the extrusion phase.