Parameter Estimation of Hybrid Dynamical Systems With Delayed Switching

In this paper, we address parameter estimation for hybrid dynamical systems with state-dependent events and time-delayed parametric switching. Parameter estimation of hybrid sys-tems can aid in system identification, model refinement, and contingency and stability analysis in various fields, including chemical, electrical, and power systems engineering. We discuss parameter estimation for hybrid systems and introduce the concept of time-delay in switching events. Hybrid systems are difficult to analyze, and complicate the calculation of trajectory sensitivities used in gradient estimation methods. We compute the proper jump conditions for these trajectory sensitivities when state-dependent, time-delayed switching occurs. While this study is fairly general to hybrid systems, it is presented with an emphasis on electric power sys-tems, whose continuous dynamics consist of power generation, transmission, and consumption, and whose discrete dynamics are governed by protection logic devices