Abstract
Behind any complex system in nature or engineering, there is an intricate network of interconnections that is often unknown. Using a control-theoretical approach, we study the problem of network reconstruction (NR): inferring both the network structure and the coupling weights based on measurements of each node's activity. We derive two new methods for NR, a low-complexity reduced-order estimator (which projects each node's dynamics to a one-dimensional space) and a full-order estimator for cases where a reduced-order estimator is not applicable. We prove their convergence to the correct network structure using Lyapunov-like theorems and persistency of excitation. Importantly, these estimators apply to systems with partial state measurements, a broad class of node dynamics and internode coupling functions, and in the case of the reduced-order estimator, node dynamics and internode coupling functions that are not fully known. The effectiveness of the estimators is illustrated using both numerical and experimental results on networks of chaotic oscillators.
| Original language | English (US) |
|---|---|
| Article number | 083121 |
| Journal | Chaos |
| Volume | 29 |
| Issue number | 8 |
| DOIs | |
| State | Published - Aug 1 2019 |
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ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy(all)
- Applied Mathematics
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Discovering the topology of complex networks via adaptive estimators. / Burbano Lombana, Daniel Alberto; Freeman, Randy A.; Lynch, Kevin M.
In: Chaos, Vol. 29, No. 8, 083121, 01.08.2019.Research output: Contribution to journal › Article
TY - JOUR
T1 - Discovering the topology of complex networks via adaptive estimators
AU - Burbano Lombana, Daniel Alberto
AU - Freeman, Randy A.
AU - Lynch, Kevin M.
PY - 2019/8/1
Y1 - 2019/8/1
N2 - Behind any complex system in nature or engineering, there is an intricate network of interconnections that is often unknown. Using a control-theoretical approach, we study the problem of network reconstruction (NR): inferring both the network structure and the coupling weights based on measurements of each node's activity. We derive two new methods for NR, a low-complexity reduced-order estimator (which projects each node's dynamics to a one-dimensional space) and a full-order estimator for cases where a reduced-order estimator is not applicable. We prove their convergence to the correct network structure using Lyapunov-like theorems and persistency of excitation. Importantly, these estimators apply to systems with partial state measurements, a broad class of node dynamics and internode coupling functions, and in the case of the reduced-order estimator, node dynamics and internode coupling functions that are not fully known. The effectiveness of the estimators is illustrated using both numerical and experimental results on networks of chaotic oscillators.
AB - Behind any complex system in nature or engineering, there is an intricate network of interconnections that is often unknown. Using a control-theoretical approach, we study the problem of network reconstruction (NR): inferring both the network structure and the coupling weights based on measurements of each node's activity. We derive two new methods for NR, a low-complexity reduced-order estimator (which projects each node's dynamics to a one-dimensional space) and a full-order estimator for cases where a reduced-order estimator is not applicable. We prove their convergence to the correct network structure using Lyapunov-like theorems and persistency of excitation. Importantly, these estimators apply to systems with partial state measurements, a broad class of node dynamics and internode coupling functions, and in the case of the reduced-order estimator, node dynamics and internode coupling functions that are not fully known. The effectiveness of the estimators is illustrated using both numerical and experimental results on networks of chaotic oscillators.
UR - http://www.scopus.com/inward/record.url?scp=85071337756&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85071337756&partnerID=8YFLogxK
U2 - 10.1063/1.5088657
DO - 10.1063/1.5088657
M3 - Article
C2 - 31472515
AN - SCOPUS:85071337756
VL - 29
JO - Chaos
JF - Chaos
SN - 1054-1500
IS - 8
M1 - 083121
ER -