Pinning Controllability of Complex Network Systems With Noise

Abstract

The ability of a network of nonlinear systems to synchronize onto the desired reference trajectory in the presence of one or more leader nodes is known as the pinning controllability problem. This paper studies the pinning controllability of multi-agent networks subject to three different types of noise diffusion processes; namely, noise affecting the node dynamics, the communication links, and the pinning control action itself. By using appropriate stochastic Lyapunov functions, sufficient pinning controllability conditions are derived depending on the node dynamics, network structure, noise intensity, and control parameters. Counterintuitively, it is found that under some specific conditions noise may enhance the pinning controllability of the network making it easier to drive all agents towards the desired collective behavior. The effectiveness of the theoretical results is illustrated via two application examples arising in the context of gene regulatory networks and synchronization of chaotic systems.

Scalability in Nonlinear Network Systems Affected by Delays and Disturbances

“…We start with illustrating the use of Proposition 3 to design protocols guaranteeing L ∞ -sIOS of network ( 7) - (8). As in [30], the parameters of the robots in ( 16) are m i = 10.1kg, I i = 0.13kgm 2 , l i = 0.12m, ∀i.…”

“…There is then no surprise that a large body of literature devoted to the study of collective network behaviours has emerged: problems such as consensus, synchronization, coordination, have attracted much research attention and results have been obtained under a wide range technical conditions, see e.g. [6]- [8].…”

Finite-HorizonH∞State Estimation for Stochastic Coupled Networks With Random Inner Couplings Using Round-Robin Protocol

“…In some practical situations, however, the inner connections between nodes might be uncertain and expose certain switching/random behaviors owing to a variety of reasons such as network congestion, random failures, unknown but sudden changes of the working conditions as well as the unexpected environmental changes. In view of this, particular attention has been paid to the investigation on the impact from the uncertain/random/switching couplings on network dynamics [3], [6], [15], [19], [20], [30]. For example, in [22], the coupling strengths have been characterized as a uncertain term and the resulting uncertainties have been dealt with using the H ∞ performance requirements on the filtering error dynamics.…”

Pinning Control for the p53-Mdm2 Network Dynamics Regulated by p14ARF

“…On the other hand, control theory has rapidly developed for complex networks (Wang and Chen, 2002 ; Sorrentino et al, 2007 ; Liu and Barabási, 2016 ). Recently, research focuses on the important issue of how to incorporate control techniques for biological systems and networks (Nowzari et al, 2016 ; Vinayagam et al, 2016 ; Gao et al, 2017 ; Jiao et al, 2018 ; Papatsenko et al, 2018 ; Wang et al, 2019 ), such as pinning control for gene regulatory networks (Lin et al, 2014 ; Chen et al, 2016 ; Yue et al, 2017 ; Li et al, 2018 ; Burbano et al, 2019 ). In Lin et al ( 2014 ), a Boolean network model to reproduce the two-phase dynamics of the p53 network in response to DNA damage is developed.…”

“…In Li et al ( 2018 ), a single-input pinning controller design for reachability of Boolean networks is proposed; in addition, different nodes are selected as the pinning ones by solving logical matrix equations and Drosophila melanogaster gene regulatory network is used to illustrate the effectiveness and feasibility of the developed method. Finally, Burbano et al ( 2019 ) pinning controllability analysis of multiagent networks subjected to three different types of noise diffusion processes; namely, noise affecting the node dynamics, the communication links, and the pinning control action is done, the effectiveness of the theoretical results is illustrated in the genetic Toggle Switch, originally introduced in E. coli . This last publication uses a model based on stochastic differential equations.…”