MPEC strategies for optimization of a class of hybrid dynamic systems

With the development and widespread use of large-scale nonlinear programming (NLP) tools for process optimization, there has been an associated application of NLP formulations with complementarity constraints in order to represent discrete decisions. In particular, these constraints arise frequently in equation-based formulations for real-time optimization. Also known as mathematical programs with equilibrium constraints (MPECs), these formulations can be used to model certain classes of discrete events and can be more efficient than a mixed integer formulation, particularly for large systems with many discrete decisions, such as dynamic systems with switches at any point in time. In this study, we consider and extend MPEC formulations for the optimization of a class of hybrid dynamic models, where the differential states remain continuous over time. These include differential inclusions of the Filippov type. Here, particular care is required in the formulation in order to preserve smoothness properties of the dynamic system. Results on three case studies, including process control examples, illustrate the effectiveness and accuracy of the proposed MPEC optimization methodology for a class of hybrid dynamic systems.