Distributed-Observer-Based Distributed Control Law for Affine Nonlinear Systems and Its Application on Interconnected Cruise Control of Intelligent Vehicles

Abstract

Distributed-observer-based distributed control law for interconnected systems has become the research focus in recent years. This paper extends this study from linear systems to a class of affine nonlinear systems. Before this, distributed observer for nonlinear systems with control inputs has not been studied, as well as the distributed-observer-based distributed control law. To fill this gap, we overcome the difficulty of proving joint observability for distributed nonlinear observer by an original analysis method based on maximum invariant distribution. In addition, the influence of model mismatch on distributed observer and distributed controller is also investigated and analyzed in detail. By analyzing the complex coupling relationship between observer dynamics, control input, and model mismatch, we successfully deal with the dissatisfaction of separation principle and prove the stability of observer error systems and closed-loop systems. The results show both the error dynamics of distributed observer and the system states of closed-loop system formed by the observer-based distributed control law can converge to an arbitrarily small invariant set around the origin. In addition to the original work in distributed-observer-based distributed control law, this paper also contributes to the design of distributed observer. Firstly, the proposed design method is also applicable to distributed observer of autonomous systems. Compared to the existing results, our method admits weaker assumptions. Specifically, one could find an approximate system to meet the assumptions required by designing distributed observer when the underlying system fails to meet the requirements. At last, the automated highway system is employed to verify the results.