Parameter estimation in delayed-switching hybrid dynamical systems

This paper addresses parameter estimation for hybrid dynamical systems, such as electric power systems, with state-dependent events and time-delayed parametric switching. Previous work dealing with hybrid dynamical systems has addressed the calculation of trajectory sensitivities used in gradient-based parameter estimation methods, as well as the computation of proper sensitivity jump conditions at switching events. We extend this work by allowing for state-dependent delay and cancellation of switching events, and by modifying the jump conditions accordingly. We also discuss the treatment of non-triggered events, the calculation of sensitivities with respect to event times and post-switch parameter values, and the use of asynchronously sampled data. A simulation study on the IEEE 39-bus power system is presented to demonstrate the estimation of parameters as the system undergoes delayed switching events.