On computing sensitivities for parameter estimation in hybrid systems

Inverse problems have received much attention. In these problems, one deals with a mathematical model and attempts to identify unknown parameters in the model based on certain observations of the underlying phenomenon. Most often, these problems are formulated as optimization problems in an infinite dimensional state space where one must determine the parameter from some admissible parameter set that minimizes the given cost function. Quasilinearization has been shown to be an effective to system identification problems. Although quasilinearization has been used quite successfully, implementation requires certain smoothness properties of the state with respect to the unknown parameter. In fact, the success of quasilinearization depends on the accurate determination of the derivative of the state with respect to the unknown parameter, i.e. the sensitivity. In this short note we use a finite element method to directly solve the sensitivity equations for the state sensitivity and compare the results to brute force finite difference methods