Distributed control for a class of nonlinear systems based on distributed high-gain observer

This paper concerns the problem of designing distributed control law for a class nonlinear system in which the measurement outputs of the system are distributed in different subsystems. It leads to a challenge that the states of the original systems cannot be completely reconstructed by any single subsystem. In order to solve this problem, distributed state observers and the distributed observer-based distributed control problem emerges as the times require. However, the distributed observers problem of the nonlinear systems is rarely studied, and the distributed control law formed by distributed nonlinear observers has hardly ever been studied up to now. To this end, this paper develops the distributed high-gain observers for a class of nonlinear systems. Unlike the previous several results, our study has the ability to deal with model uncertainty, and devotes itself to overcoming the problem that the separation principle is not tenable. In addition, based on the state estimate generated by the designed distributed observer, an output feedback control law formed by applying the state estimate is developed. Furthermore, a class of sufficient conditions is proved for guaranteeing the error dynamics of the distributed observer and the state trajectory of the closed-loop system to enter an arbitrary small invariant set around the origin. Finally, the simulation results verify the effectiveness of the proposed method.