This paper formulates and solves a new problem of the double model following adaptive control (MFAC) of nodes and links in a complex dynamical network (CDN). This is different from most existing studies on CDN and MFAC. Inspired by the concept of composite systems, the CDN with dynamic links is regarded as an interconnected system composed of an interconnected node group (NG) and link group (LG). Guided by the above-mentioned new idea of viewing a CDN from the perspective of composite systems, by means of Lyapunov theory and proposed related mathematical preliminaries, a new adaptive control scheme is proposed for NG. In addition, to remove the restriction that the states of links in a CDN are unavailable due to physical constraints, technical restraints, and expensive measurement costs, we synthesize the coupling term in LG with the proposed adaptive control scheme for NG, such that the problem of double MFAC of nodes and links in CDN is solved. Finally, a simulation example is presented to verify the theoretical results.
This article formulates and solves a problem of model following adaptive control (MFAC) of nodes in the complex dynamic network (CDN) with the dynamic matrix-relation links. From the perspective of composite systems, the CDN with the dynamic matrix-relation links is considered as an interconnected system composed of intercoupling node subsystem (NS) and link subsystem (LS). Based on this idea, employing the Riccati matrix differential equation as the dynamic equation of LS, and the vector differential equation with the second derivative term as the dynamic equation of NS. Then, to remove the restriction that the state of LS is unavailable, an adaptive control scheme is proposed for NS with the help of constructed dynamic auxiliary tracking target for LS, such that the problem of MFAC of nodes is solved. Besides, it is proved mathematically that the state of NS is asymptotically tracking the state of the given reference model when the state of LS is asymptotically tracking the constructed dynamic auxiliary tracking target. Finally, the numerical simulation is given to verify the effectiveness of the theoretical results in this article.
Geometrically, a complex dynamical network (CDN) can be regarded as the
interconnected system composed of the node subsystem (NS) and the link
subsystem (LS) coupled with each other. Guided by this idea, in order to
achieve the goal of each node following asymptotically its own reference
target in a CDN, this paper investigates the model following adaptive
control (MFAC) problem of NS via the dynamics of links, which implies
that the LS plays the important dynamic auxiliary role in the MFAC
realization of nodes. Meanwhile, we focus on the condition that the
links state information is unavailable, due to sensor practical
application and measurement cost constraints. To obviate this
restriction, we construct the asymptotical state observer for the LS.
Next, to achieve the control goal of this paper, an appropriate Lyapunov
candidate function is selected, by which the MFAC scheme for NS is
synthesized based on the state observer of LS. Finally, the simulation
example is performed to demonstrate the theoretical results in this
paper.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.