Synchronization and Dynamic Consensus of Heterogeneous Networked Systems

Abstract

We present an analysis framework for the study of synchronization of heterogeneous nonlinear systems interconnected over networks described by directed graphs. Heterogeneous systems may have totally different dynamical models, albeit of the same dimension, or may possess equal models with different lumped parameters. We show that their behavior, when network-interconnected, is fully characterized in terms of two properties whose study may be recasted in terms of the stability analysis of two corresponding interconnected dynamical systems that evolve in orthogonal spaces: on one hand, we have the so-called emergent dynamics and, on the other, the synchronization error dynamics. Based on this premise, we introduce the concept of dynamic consensus and we present results on robust stability which assess the conditions for practical asymptotic synchronization of networked systems and characterize their collective behavior. To illustrate our main theoretical findings we broach a brief case-study on mutual synchronization of heterogeneous chaotic oscillators.

Synchronization in Networks of Identical Nonlinear Systems via Dynamic Dead Zones

“…As already established in [13], when w = 0, the triangular structure in (11), Assumption 2 applied to the x 1 -dynamics, and inequality (22) allow concluding global exponential stability of the set X. Moreover, when w = 0, ISS of the set X can be proved by using again (22) and standard Lypaunov arguments (see, e.g., [29,Chapter 10] for further details).…”

“…Thus convergence to the forward invariant set X is established. To this end, we recall the result from [13], which provides a suitable choice of the diffusing coupling K establishing exponential stability of the e-dynamics (11). We also report the main steps of the proof given in [13] which are instrumental to the main result of this work, see Section III.…”

“…At the same time, the community extended the linear resulst to the nonlinear context. Among others, it is worth mentioning [9], where the author exploits passivity tools, [10] with dissipativity theory, and [11], where the authors use high-gain arguments. Nowadays, many the results of the linear framework have been successfully extended to the nonlinear setting [12], [13].…”

A tool for analysis and synthesis of heterogeneous multi-agent systems under rank-deficient coupling

“…This notion has already appeared in (Kim, Yang, Kim, & Shim, 2012) for scalar linear systems, and in (Kim, Yang, Shim, & Kim, 2013;Kim, Yang, Shim, Kim, & Seo, 2016b) for scalar nonlinear systems under the terminology "averaged dynamics." More recently, Panteley, Loría, & Conteville (2015) introduced a notion called "emergent dynamics" (see also (Panteley & Loría, 2017)), which is, however, different from the blended dynamics in the sense that it is not a multi-agent system. Moreover, they require stability of zero-dynamics in each agent and they take the average of the zero-dynamics when the emergent dynamics is constructed.…”

Quasi‐synchronization of multilayer heterogeneous networks with a dynamic leader

“…There are many researches on heterogeneous networks of first‐order dynamics. By taking into account the network structure, the dynamics of different nodes and the interconnections among the nodes, synchronization of heterogeneous nonlinear networks with directed topology has been investigated in Reference . Furthermore, many investigations have been performed to extend the researches of first‐order systems to higher order (second) systems.…”