Tracking control for a class of uncertain complex dynamical networks with outgoing links dynamics

Abstract

A complex dynamical network (CDN) can be considered as the composition system with the nodes subsystem (NS) and the links subsystem (LS), and both subsystems are coupled with each other. In this paper, two vector differential equations (VDE) are used to describe the dynamical behaviours of NS and LS, respectively, in which the dynamical behaviour of NS is considered as the VDE with the second derivative term (SDT). This paper mainly focuses on the dynamics of LS, which is represented as VDE with the intuitive topologic feature of outgoing links, and investigates the design of the tracking controller for NS and the auxiliary tracking objectives (ATO) for LS. Firstly, the dynamical models of NS and LS in CDN are proposed, and the corresponding assumptions are given. Secondly, based on Lyapunov stability theory, the controller of NS and the ATO of LS are designed so that the state of NS can asymptotically track the given reference signal. Finally, the effectiveness of the proposed control strategy in this paper is verified by the numerical simulation example with N two-links robots.

Abbreviations: ATO: auxiliary tracking objectives; CDN: complex dynamical network; LS: links subsystem; MDE: matrix differential equation; NS: nodes subsystem; SDT:second derivative term; VDE: vector differential equation;

Keywords:

• Complex dynamical network
• nodes subsystem
• links subsystem
• tracking control
• auxiliary tracking objectives

Disclosure statement

The authors declare no potential conflict of interests.

Data avaliability statement

The data used to support the findings of this study are available from the first author upon request.

Additional information

Funding

This work was supported by National Natural Science Foundation of China [grant number 61673120] Key Laboratory of Intelligent Manufacturing Technology (Shantou University), Ministry of Education of China [grant number 202109242] Team Project of Universities of Guangdong Province under Grant [grant number 2015KCXTD018] Guangdong Basic and Applied Basic Research Foundation [grant number 2020A1515010809].