On the Design of Distributed Observers for Nonlinear Systems

In this paper, we investigate the distributed state estimation problem for a nonlinear dynamical system. Relying upon the assumption of the existence of a block-triangular ``uniform observability" canonical form, local high-gain observers are used to stabilize the estimation error for the observable portion of the state and exchange of information between neighbors is used to achieve consensus in the estimation of the state of the unobservable part. The paper addresses first the case of an autonomous system, and then the case of a controlled dynamical system under the assumption that the exogenous input is accessible by each node in the network. Based on the designed state estimator, each distributed sensor node can achieve asymptotic estimation of the full state, with an arbitrarily fixed decay rate of the observation error.