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The frequency-domain technique, commonly used in analyzing and designing feedback control systems, is effective for linear, time-invariant systems. However, it falls short when dealing with nonlinear, time-varying, and multiple-input multiple-output systems. The time-domain or state-space approach addresses these limitations by utilizing state variables to construct simultaneous, first-order differential equations, known as state equations, for an nth-order system.
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Updated: Jan 13, 2026

Inherent Dynamics Visualizer, an Interactive Application for Evaluating and Visualizing Outputs from a Gene Regulatory Network Inference Pipeline
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Tracking control of complex dynamical networks via reservoir computing.

Guyue Wu1, Longkun Tang1, Wei Zhao2

  • 1School of Mathematical Science, Huaqiao University, Quanzhou 362021, China.

Chaos (Woodbury, N.Y.)
|January 12, 2026
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Summary
This summary is machine-generated.

This study introduces a data-driven tracking control method using reservoir computing (RC) for complex dynamical networks. The technique effectively controls both homogeneous and heterogeneous networks into desired trajectories, even with partial state observation.

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Area of Science:

  • Complex Systems
  • Network Science
  • Control Theory

Background:

  • Networked systems exhibit complex collective behaviors due to inter-node interactions, making tracking control challenging.
  • Existing control methods for single systems are insufficient for complex networked dynamics.

Purpose of the Study:

  • To extend data-driven tracking control to networked systems using reservoir computing (RC).
  • To develop an RC-based control technique for complex dynamical networks, including homogeneous and heterogeneous nodes.
  • To enable trajectory control even with partially observable node states.

Main Methods:

  • Utilized reservoir computing (RC) for data-driven control of networked systems.
  • Developed a novel RC-based control scheme applicable to complex dynamical networks.
  • Validated the approach through extensive simulations on various network structures.

Main Results:

  • The proposed RC-based control successfully guided networks (homogeneous and heterogeneous) to desired trajectories.
  • The control scheme demonstrated effectiveness across diverse network structures and coupling strengths.
  • The method showed good robustness against measurement noise in networked systems.

Conclusions:

  • The developed RC-based control technique is a feasible and effective solution for tracking control in complex dynamical networks.
  • This approach offers a powerful tool for controlling networked systems with partial observability.
  • The robustness against noise highlights its practical applicability in real-world scenarios.