Robust Parameter Estimation for Hybrid Dynamical Systems

TL;DR

This paper introduces a hybrid estimation algorithm for hybrid dynamical systems that guarantees convergence of unknown parameters during both continuous and discrete system evolutions, with proven stability and demonstrated effectiveness in simulations.

Contribution

It presents a novel hybrid estimation method that operates during flows and jumps, ensuring parameter convergence under hybrid persistence of excitation.

Findings

Guarantees convergence of parameter estimates

Proves input-to-state stability under disturbances

Demonstrates effectiveness in spacecraft simulation

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. 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.