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Simultaneous Topology Estimation and Synchronization of Dynamical Networks with Time-varying Topology

Nana Wang, Esteban Restrepo, Dimos V. Dimarogonas

TL;DR

This work proposes an adaptive control strategy for the simultaneous estimation of topology and synchronization in complex dynamical networks with unknown, timevarying topology, utilizing an edge-agreement framework.

Abstract

We propose an adaptive control strategy for the simultaneous estimation of topology and synchronization in complex dynamical networks with unknown, time-varying topology. Our approach transforms the problem of time-varying topology estimation into a problem of estimating the time-varying weights of a complete graph, utilizing an edge-agreement framework. We introduce two auxiliary networks: one that satisfies the persistent excitation condition to facilitate topology estimation, while the other, a uniform-$δ$ persistently exciting network, ensures the boundedness of both weight estimation and synchronization errors, assuming bounded time-varying weights and their derivatives. A relevant numerical example shows the efficiency of our methods.

Simultaneous Topology Estimation and Synchronization of Dynamical Networks with Time-varying Topology

TL;DR

This work proposes an adaptive control strategy for the simultaneous estimation of topology and synchronization in complex dynamical networks with unknown, timevarying topology, utilizing an edge-agreement framework.

Abstract

We propose an adaptive control strategy for the simultaneous estimation of topology and synchronization in complex dynamical networks with unknown, time-varying topology. Our approach transforms the problem of time-varying topology estimation into a problem of estimating the time-varying weights of a complete graph, utilizing an edge-agreement framework. We introduce two auxiliary networks: one that satisfies the persistent excitation condition to facilitate topology estimation, while the other, a uniform- persistently exciting network, ensures the boundedness of both weight estimation and synchronization errors, assuming bounded time-varying weights and their derivatives. A relevant numerical example shows the efficiency of our methods.
Paper Structure (7 sections, 1 theorem, 14 equations)

This paper contains 7 sections, 1 theorem, 14 equations.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Notations
  4. Model and problem formulation
  5. Topology estimation under bounded time-varying weights
  6. Control design and weight estimation laws
  7. Time-varying topology estimation

Key Result

Proposition 1

Assume that the signal $\hat{Z}(t)$ is bounded, globally Lipschitz and satisfies that for any unit vector $v \in \mathbb{R}^{\bar{M}}$ where $T, \mu>0$. With Assumptions n182 and assumption_weight, the edge weight estimation errors $\tilde{w}(t)$ of the multi-agent system 108 are globally ultimately bounded, and all the closed-loop signals are bounded, after applying update law 170 and the control

Theorems & Definitions (3)

  • Remark 1
  • Proposition 1
  • proof