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

Distributed-observer-based distributed control law for interconnected systems has become the research focus in recent years, owing to its broad prospects. This paper extends the objectives of this study from linear systems to a class of affine nonlinear systems. Before this, distributed observer for nonlinear systems with controlled 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 the joint observability of distributed observer for nonlinear systems by an original analysis method based on maximum invariant distribution. Furthermore, to deal with the dissatisfaction of the separation principle, a high-gain parameter is introduced in the distributed observer. In addition, the influence of model mismatch on the distributed observer and distributed controller is also investigated and analyzed in detail. By analyzing the complex coupling relationship between observer dynamics, control input, high-gain parameter, and model mismatch, we successfully prove the asymptotic omniscience of distributed observer and the stability of closed-loop systems. The results show that both the error dynamics of the distributed observer and the system states of the 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 has innovation in the design of distributed observer. Firstly, the proposed design method is also applicable to the distributed observer of autonomous systems. Compared to existing results on autonomous systems, 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 interconnected cruise control of intelligent vehicles is employed to be verified the developed results.