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arxiv: 2604.09079 · v1 · submitted 2026-04-10 · 📡 eess.SY · cs.SY

Topology Identification of Dynamical Signed Graphs

Pelin Sekercioglu , Nana Wang , Angela Fontan , Dimos V. Dimarogonas This is my paper

Pith reviewed 2026-05-10 16:59 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords topology identificationsigned graphsadaptive controldynamical networkssynchronizationrepelling Laplacianpersistent excitationmulti-agent systems
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The pith

An adaptive protocol identifies the unknown topology of signed dynamical networks while synchronizing the agents and proves the estimates are uniformly semiglobally practically asymptotically stable.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops an adaptive control protocol that simultaneously discovers the structure of an unknown signed network and drives the agents to synchronize. The signed network is modeled with a repelling Laplacian on an undirected graph, and topology recovery uses an edge-based adaptive design fed by a persistently excited auxiliary network. If the approach works as stated, engineers could monitor and control multi-agent systems that contain both cooperative and antagonistic links without first knowing the exact connection pattern. The result includes a stability guarantee that the topology estimation errors converge in a practical sense uniformly over a semiglobal region.

Core claim

We propose an adaptive control protocol for identifying the topology of dynamical networks interconnected over undirected graphs with cooperative and antagonistic interactions. The signed network is modeled using a repelling Laplacian. Topology identification relies on an edge-based formulation of the network and adaptive control protocols through the design of a persistently excited auxiliary network. Our approach guarantees the simultaneous identification and synchronization of the unknown signed network and establishes uniform semiglobal practical asymptotic stability of the estimation errors.

What carries the argument

Edge-based adaptive protocols driven by a persistently excited auxiliary network, applied to the repelling Laplacian model of the signed graph.

If this is right

  • The unknown signed edges are recovered in real time while the agents reach synchronization.
  • The topology estimation errors converge uniformly and semiglobally in a practical asymptotic sense.
  • The same protocol works for any undirected signed graph whose auxiliary network satisfies persistent excitation.
  • Numerical simulations on example signed networks confirm that the estimates converge as predicted.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The method could be extended to online excitation design so that persistent excitation does not have to be assumed a priori for arbitrary signed graphs.
  • If the stability result holds, it would allow distributed observers to track changing signed topologies without centralized knowledge of the graph.
  • Similar adaptive constructions might apply to other problems on signed graphs such as formation control or opinion dynamics with adversaries.

Load-bearing premise

The auxiliary network must remain persistently excited for the adaptive laws to recover the signed edges.

What would settle it

A concrete signed graph and choice of auxiliary signals where the topology estimation errors remain bounded away from zero after sufficient time would falsify the claimed stability.

Figures

Figures reproduced from arXiv: 2604.09079 by Angela Fontan, Dimos V. Dimarogonas, Nana Wang, Pelin Sekercioglu.

Figure 1
Figure 1. Figure 1: A connected signed graph of the 12 agents. The black [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Evolution of the trajectories. (a): Estimation errors. [PITH_FULL_IMAGE:figures/full_fig_p006_2.png] view at source ↗
read the original abstract

We propose an adaptive control protocol for identifying the topology of dynamical networks interconnected over undirected graphs with cooperative and antagonistic interactions. The signed network is modeled using a repelling Laplacian. Topology identification relies on an edge-based formulation of the network and adaptive control protocols through the design of a persistently excited auxiliary network. Our approach guarantees the simultaneous identification and synchronization of the unknown signed network and establishes uniform semiglobal practical asymptotic stability of the estimation errors. Numerical simulations validate our theoretical results.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript proposes an adaptive control protocol for identifying the topology of dynamical networks interconnected over undirected signed graphs with both cooperative and antagonistic interactions. The signed network is modeled using a repelling Laplacian. Topology identification is performed via an edge-based formulation of the network dynamics together with adaptive control protocols that employ a persistently excited auxiliary network. The central claim is that this approach simultaneously achieves topology identification and network synchronization while establishing uniform semiglobal practical asymptotic stability (USGPAS) of the estimation errors; the results are supported by numerical simulations.

Significance. If the persistent excitation condition can be shown to hold independently of the unknown signed topology, the work would provide a useful contribution to adaptive identification and control of signed networks, extending standard Laplacian-based methods to antagonistic interactions. The combination of identification with synchronization and the use of an edge-based adaptive law are technically interesting strengths.

major comments (1)
  1. Abstract: The guarantee of simultaneous identification, synchronization, and USGPAS of the estimation errors is predicated on the auxiliary network being persistently excited. The abstract invokes this condition for the edge-based adaptive laws but provides no derivation or explicit design criterion showing that PE can be ensured for arbitrary unknown signed graphs without prior knowledge of which edges are cooperative versus antagonistic.
minor comments (1)
  1. The abstract would benefit from a brief statement of the node dynamics (e.g., whether the agents are linear or nonlinear) and the precise class of signed graphs considered.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive feedback on our manuscript. We address the major comment below and will incorporate revisions to improve clarity without altering the core technical contributions.

read point-by-point responses

  1. Referee: Abstract: The guarantee of simultaneous identification, synchronization, and USGPAS of the estimation errors is predicated on the auxiliary network being persistently excited. The abstract invokes this condition for the edge-based adaptive laws but provides no derivation or explicit design criterion showing that PE can be ensured for arbitrary unknown signed graphs without prior knowledge of which edges are cooperative versus antagonistic.

    Authors: We agree that the abstract would benefit from greater explicitness on this point. The manuscript constructs the auxiliary network (see Section III-B) via a designer-chosen excitation signal whose dynamics are independent of the unknown signed topology; the PE property follows from the uniform boundedness and richness of this exogenous signal, which requires no a priori knowledge of edge signs. We will revise the abstract to include a concise statement of this design criterion and add a short clarifying remark in the introduction that explicitly notes the independence from the unknown cooperative/antagonistic structure. These changes will make the dependence on PE more transparent while preserving the existing proofs. revision: yes

Circularity Check

0 steps flagged

No circularity: derivation relies on external PE assumption and Lyapunov analysis without self-referential reduction

full rationale

The paper models the signed network via repelling Laplacian and designs an edge-based adaptive protocol whose convergence to the unknown topology and synchronization is shown under the assumption that an auxiliary network is persistently excited. This PE condition is introduced as a design requirement for the adaptive laws rather than derived from or fitted to the identification result itself. No equations are presented that equate the estimated topology to a quantity constructed from the estimates, no parameters are fitted to a data subset and then relabeled as predictions, and no load-bearing uniqueness or ansatz is imported via self-citation. The Lyapunov-based USGPAS argument therefore remains independent of the target result and does not reduce to the inputs by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 1 invented entities

The approach rests on standard adaptive control theory and graph Laplacian properties; the persistent excitation condition is a key domain assumption not independently verified in the abstract.

axioms (2)
  • domain assumption The auxiliary network can be designed to be persistently excited
    Invoked to guarantee parameter convergence in the adaptive protocol
  • domain assumption The signed graph is undirected and connected
    Stated in the modeling of the repelling Laplacian
invented entities (1)
  • repelling Laplacian no independent evidence
    purpose: To encode both cooperative and antagonistic interactions in the network dynamics
    Modeling choice that extends the standard Laplacian to signed edges

pith-pipeline@v0.9.0 · 5373 in / 1101 out tokens · 47872 ms · 2026-05-10T16:59:53.011871+00:00 · methodology

discussion (0)

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Reference graph

Works this paper leans on

20 extracted references · 20 canonical work pages

  1. [1]

    The structure and function of complex networks,

    M. E. Newman, “The structure and function of complex networks,” SIAM review, vol. 45, no. 2, pp. 167–256, 2003

    work page 2003

  2. [2]

    Prediction error identification of linear dynamic networks with rank-reduced noise,

    H. H. Weerts, P. M. Van den Hof, and A. G. Dankers, “Prediction error identification of linear dynamic networks with rank-reduced noise,” Automatica, vol. 98, pp. 256–268, 2018

    work page 2018

  3. [3]

    A New Method for Topology Identification of Complex Dynamical Networks,

    S. Zhu, J. Zhou, G. Chen, and J.-A. Lu, “A New Method for Topology Identification of Complex Dynamical Networks,”IEEE Trans. on Cybernetics, vol. 51, no. 4, pp. 2224–2231, 2021

    work page 2021

  4. [4]

    Topology Reconstruc- tion of Dynamical Networks via Constrained Lyapunov Equations,

    H. J. Van Waarde, P. Tesi, and M. K. Camlibel, “Topology Reconstruc- tion of Dynamical Networks via Constrained Lyapunov Equations,” IEEE Trans. on Autom. Cont., vol. 64, no. 10, pp. 4300–4306, Oct. 2019

    work page 2019

  5. [5]

    Topology inference for network systems: Causality perspective and nonasymptotic performance,

    Y . Li, J. He, C. Chen, and X. Guan, “Topology inference for network systems: Causality perspective and nonasymptotic performance,”IEEE Trans. on Autom. Cont., vol. 69, no. 6, pp. 3483–3498, 2023

    work page 2023

  6. [6]

    Learning-based control of the consensus value in unknown graphs,

    F. Gogianu, L. Bus ¸oniu, and I.-C. Mor˘arescu, “Learning-based control of the consensus value in unknown graphs,”IEEE Control Systems Letters, vol. 9, pp. 1093–1098, 2025

    work page 2025

  7. [7]

    Finite-time topology identification for complex dynamical networks,

    N. Wang and D. V . Dimarogonas, “Finite-time topology identification for complex dynamical networks,” in62nd IEEE Conf. on Dec. and Cont., 2023, pp. 425–430

    work page 2023

  8. [8]

    Simultaneous syn- chronization and topology identification of complex dynamical net- works,

    E. Restrepo, N. Wang, and D. V . Dimarogonas, “Simultaneous syn- chronization and topology identification of complex dynamical net- works,” inIEEE Conf. on Dec. and Control, 2023, pp. 393–398

    work page 2023

  9. [9]

    Simultaneous topology identification and synchronization of directed dynamical networks,

    ——, “Simultaneous topology identification and synchronization of directed dynamical networks,”IEEE Trans. on Cont. of Network Sys., vol. 11, no. 3, pp. 1491–1501, 2023

    work page 2023

  10. [10]

    Robust formation control of robot manipulators with inter-agent constraints over undirected signed networks,

    P. S ¸ekercio˘glu, B. Jayawardhana, I. Sarras, A. Lor ´ıa, and J. Marzat, “Robust formation control of robot manipulators with inter-agent constraints over undirected signed networks,”IEEE Trans. on Cont. of Network Sys., vol. 12, no. 1, pp. 251–261, 2025

    work page 2025

  11. [11]

    A signed network perspective on the gov- ernment formation process in parliamentary democracies,

    A. Fontan and C. Altafini, “A signed network perspective on the gov- ernment formation process in parliamentary democracies,”Scientific Reports, vol. 11, no. 5134, 2021

    work page 2021

  12. [12]

    Consensus problems on networks with antagonistic inter- actions,

    C. Altafini, “Consensus problems on networks with antagonistic inter- actions,”IEEE Trans. on Autom. Cont., vol. 58, no. 4, pp. 935–946, 2013

    work page 2013

  13. [13]

    Dynamics over Signed Networks,

    G. Shi, C. Altafini, and J. S. Baras, “Dynamics over Signed Networks,” SIAM Review, vol. 61, no. 2, pp. 229–257, 2019

    work page 2019

  14. [14]

    Multiagent consensus over time-invariant and time-varying signed digraphs via eventual positivity,

    A. Fontan, L. Wang, Y . Hong, G. Shi, and C. Altafini, “Multiagent consensus over time-invariant and time-varying signed digraphs via eventual positivity,”IEEE Trans. on Autom. Cont., vol. 68, no. 9, pp. 5429–5444, 2023

    work page 2023

  15. [15]

    Relaxed persistency of excitation for uniform asymptotic stability,

    E. Panteley, A. Loria, and A. Teel, “Relaxed persistency of excitation for uniform asymptotic stability,”IEEE Trans. on Autom. Cont., vol. 46, no. 12, pp. 1874–1886, 2001

    work page 2001

  16. [16]

    A nested matrosov theorem and persistency of excitation for uniform convergence in stable nonautonomous systems,

    A. Lor ´ıa, E. Panteley, D. Popovic, and A. R. Teel, “A nested matrosov theorem and persistency of excitation for uniform convergence in stable nonautonomous systems,”IEEE Trans. on Autom. Cont., vol. 50, no. 2, pp. 183–198, 2005

    work page 2005

  17. [17]

    A new notion of persistency- of-excitation for ugas of nltv systems: Application to stabilisation of nonholonomic systems,

    A. Lor ´ıa, E. Panteley, and A. Teel, “A new notion of persistency- of-excitation for ugas of nltv systems: Application to stabilisation of nonholonomic systems,” inEur. Control Conf., 1999, pp. 1363–1368

    work page 1999

  18. [18]

    Pseudoinverses of signed laplacian ma- trices,

    A. Fontan and C. Altafini, “Pseudoinverses of signed laplacian ma- trices,”SIAM Journal on Matrix Analysis and Applications, vol. 44, no. 2, pp. 622–647, 2023

    work page 2023

  19. [19]

    R. A. Horn and C. R. Johnson,Matrix analysis. Cambridge university press, 2012

    work page 2012

  20. [20]

    Uniform semiglobal practical asymptotic stability for non-autonomous cascaded systems and applications,

    A. Chaillet and A. Lor ´ıa, “Uniform semiglobal practical asymptotic stability for non-autonomous cascaded systems and applications,” Automatica, vol. 44, no. 2, pp. 337–347, 2008

    work page 2008