Robust parameter estimation for hybrid dynamical systems with linear parametric uncertainty

Abstract

We consider the problem of estimating a vector of unknown constant parameters for a class of hybrid dynamical systems – that is, systems whose state variables exhibit both continuous (flow) and discrete (jump) evolution – with dynamics that depend linearly on the unknown parameters. Using a hybrid systems framework, we propose a hybrid estimation algorithm that can operate during both flows and jumps that, under a notion of hybrid persistence of excitation, guarantees convergence of the parameter estimate to the true value. Furthermore, we show that the parameter estimate is input-to-state stable with respect to a class of hybrid disturbances. Simulation results including a spacecraft application show the merits of our proposed approach.