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Nonlinear control of networked dynamical systems.

Megan Morrison1, J Nathan Kutz1

  • 1Department of Applied Mathematics, University of Washington, Seattle, WA, 98195 USA.

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|May 17, 2021
PubMed
Summary
This summary is machine-generated.

We developed a mathematical framework to control complex nonlinear systems. This method uses dimensionality reduction and bifurcation theory to find control signals for manipulating system behavior between desired states.

Keywords:
Nonlinear control systemsbifurcationlimit-cyclesopen-loop systemspulse-based switching

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Area of Science:

  • Control Theory
  • Applied Mathematics
  • Network Science

Background:

  • Controlling high-dimensional nonlinear dynamical systems is challenging.
  • Existing methods often struggle with system complexity and scalability.
  • Understanding system dynamics is crucial for effective manipulation.

Purpose of the Study:

  • To develop a principled mathematical framework for controlling nonlinear, networked dynamical systems.
  • To enable manipulation of system behavior between desired fixed points.
  • To integrate dimensionality reduction, bifurcation theory, and model discovery for control.

Main Methods:

  • Dimensionality reduction to identify low-dimensional subspaces.
  • Sparse Identification of Nonlinear Dynamics (SINDy) for model fitting.
  • Bifurcation theory to compute control signals for state transitions.

Main Results:

  • A framework for computing feed-forward control signals in low-dimensional subspaces.
  • Successful projection of control signals back to high-dimensional spaces.
  • Demonstrated control in low-dimensional biological systems and high-dimensional networks.

Conclusions:

  • The developed framework offers a robust method for controlling complex nonlinear systems.
  • The approach effectively leverages system's fixed points for targeted state manipulation.
  • This work provides a pathway for designing effective controllers for networked dynamical systems.