Completely Distributed State Estimation for Jointly Observable Uncertain Linear Systems

This article presents a novel design of a distributed adaptive observer for distributed state estimation of continuous-time uncertain linear time-invariant systems over directed networks. In contrast to existing works, the observed system is subject to uncertainties and possibly jointly observable. The distributed estimation of such systems allows practical applications in challenging problems subject to sparse arrangement of sensors and model uncertainties. A class of fully distributed nonlinear adaptive observers is proposed to address these challenges. In particular, we introduce an observability decomposition method to decompose both the state and the unknown parameters of the observed system into an observable and an unobservable component. This decomposition circumvents the impact of the unknown parameters on existing observability decomposition methods. Two nonlinear mappings are designed to achieve the reconstruction of the system state and the unknown system parameters. A parametric representation of the output estimation error is established to convert the unknown parameter estimation problem of the observable subsystem into an unknown parameter identification problem using a linear regression equation. Using a Lyapunov stability analysis, it is shown that the system parameter can be recovered by the nonlinear mappings, while the distributed state estimation problem is solved.