Parameter Estimation for Hybrid Dynamical Systems with Delayed Jump Detection

We consider the problem of estimating a vector of unknown constant parameters for a class of hybrid dynamical systems with bounded delays in the detection of jumps. Using a hybrid systems framework, we propose an algorithm that estimates the jump times of the trajectories and uses stored data to update the parameter estimate at jumps. We show that the algorithm guarantees convergence of the parameter estimate to the true value, except possibly on the intervals wherein detection of jumps is delayed. Simulation results show the merits of the proposed approach.