A distributed leader‐following tracking controller using delayed control input information from neighbors. (5th August 2019)

• Record Type: Journal Article
• Authors: Zhu, Bo; Chen, Jingyang; Wang, Jia
• Other Names: Edwards Christopher guestEditor.; Simani Silvio guestEditor.
• Is Part Of: International journal of robust and nonlinear control. Volume 29:Number 16(2019)
• Page Start: 5668
• Page End: 5703
• Publication Date: 2019-08-05
• Subjects: distributed tracking -- input‐to‐state stability -- neutral‐type system -- PD control -- time delay; Automatic control -- Periodicals; Control theory -- Periodicals; Nonlinear systems -- Periodicals; 629.836
• DOI: 10.1002/rnc.4680
• Languages: English
• ISSNs: 1049-8923

Abstract

Summary: In this paper, we propose a simple, continuous, and distributed controller for the second‐order multiagent system to achieve leader‐following trajectory tracking, by exploiting the control input information of neighbors (CIIN) and using proportional‐derivative (PD) control in terms of local neighborhood synchronization error. A constant time delay is introduced in the CIIN as a design parameter to avoid the algebraic loop issue arising from the control input coupling. We develop an easily testable condition on the PD gains to ensure that the resulting neutral‐type error system is input‐to‐state stable for an arbitrary bounded delay, and prove that when the leader's acceleration is a Lipschitz continuous function with respect to time, the ultimate bound of tracking errors is strictly increasing with respect to the introduced time delay. Moreover, we analyze the robustness of the controller with respect to model uncertainties and show its potential advantages over two existing controllers in balancing the steady‐state tracking precision, the communication cost, and the continuity of controller signal. Finally, extensive simulations are conducted to show the effect of the delay on system stability, to verify the condition on PD gains, to confirm the robustness of the controller, and to demonstrate the detailed advantages.