Adaptive synchronization in networks with heterogeneous uncertain Kuramoto-like units

Abstract

We analyze adaptive synchronization capabilities in networks with Kuramoto-like units whose dynamical features are unknown and thus synchronization protocols must exhibit co-evolution capabilities. In the presence of heterogeneous and uncertain units, synchronization should be enabled by appropriate adaptive protocols that counteract the effect of heterogeneity. An interaction protocol is presented that is used by the units to communicate with each other: the protocol is based on a distributed disagreement measure. The aim of the protocol is to adapt feedback and coupling gains, so as to guarantee the emergence of a synchronous solution. The adaptive strategy is distributed, i.e. each unit self-determines the strength of its gains by using only neighboring measurements. Convergence of the synchronization error to zero is shown via Lyapunov analysis, and numerical examples demonstrate the effectiveness of the proposed protocol.

A distributed disagreement-based protocol for synchronization of uncertain heterogeneous agents

“…Future work could go in the following directions. First, it is important to investigate how to extend this protocol to nonlinear agents: a first step in this direction can be found in the companion paper [30], where the synchronization over a network of uncertain heterogeneous Kuramoto-like agents was studied. Then, the output synchronization protocol, tested only in simulations, has to be formalized and generalized to relative degree greater than one.…”

Adaptive hybrid synchronisation in uncertain Kuramoto networks with limited information

“…(see for example the full-state synchronization strategy in [16]). However, since parameter projection is fundamental for stability in the presence of quantized information as explained in the next section, then parameter projection has been introduced in Theorem 1 as well.…”

“…In line with such literature, also in the proposed protocol the knowledge of is available to all systems in the network: nevertheless, using a distributed observer, it is not difficult to extend the proposed approach to the setting where the desired reference is available to a single or to a few nodes. This issue was studied by some of the authors in [16]. With a similar smart grid application in mind, we have been focusing on frequency synchronisation, rather than on full‐state (phase and frequency) synchronisation.…”

“…As a matter of fact, stability can be achieved even without any projection (see e.g. the full‐state synchronisation strategy in [16]. However, since parameter projection is fundamental for stability in the presence of quantised information as explained in the next section, then parameter projection has been introduced in Theorem 1 as well. Remark 6 In order to implement (13), and in particular the term , it is required to communicate among neighbours the extra variable .…”

“…However, real-world networks have uncertain and heterogeneous parameters which might even change with time. Therefore, in place of static couplings, researchers have later been focusing on Kuramoto or Kuramoto-like networks characterized by evolving, adapting couplings which vary in time according to different environmental conditions, leading to the study of evolving (or adaptive) networks [14][15][16]. In [17] a simple model of adaptive Kuramoto network is given via mechanisms of homophily (reinforcing interactions with correlated units) and homeostasis (preserving the overall connection strength).…”