Abstract

We articulate an adaptive and reference-free framework based on the principle of random switching to detect and control unstable steady states in high-dimensional nonlinear dynamical systems, without requiring any a priori information about the system or about the target steady state. Starting from an arbitrary initial condition, a proper control signal finds the nearest unstable steady state adaptively and drives the system to it in finite time, regardless of the type of the steady state. We develop a mathematical analysis based on fast-slow manifold separation and Markov chain theory to validate the framework. Numerical demonstration of the control and detection principle using both classic chaotic systems and models of biological and physical significance is provided.

Original languageEnglish (US)
Article number042902
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume92
Issue number4
DOIs
StatePublished - Oct 2 2015

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Nonlinear Dynamical Systems
dynamical systems
High-dimensional
Unstable
Slow Manifold
applications of mathematics
Markov chains
Signal Control
Mathematical Analysis
Chaotic System
Markov chain
Initial conditions
Target
Arbitrary
Framework
Model

ASJC Scopus subject areas

  • Condensed Matter Physics
  • Statistical and Nonlinear Physics
  • Statistics and Probability

Cite this

Detection meeting control : Unstable steady states in high-dimensional nonlinear dynamical systems. / Ma, Huanfei; Ho, Daniel W C; Lai, Ying-Cheng; Lin, Wei.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 92, No. 4, 042902, 02.10.2015.

Research output: Contribution to journalArticle

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