Detection meeting control: Unstable steady states in high-dimensional nonlinear dynamical systems

Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Oct;92(4):042902. doi: 10.1103/PhysRevE.92.042902. Epub 2015 Oct 2.

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.

Publication types

  • Research Support, Non-U.S. Gov't
  • Research Support, U.S. Gov't, Non-P.H.S.
  • Validation Study

MeSH terms

  • Animals
  • Cell Differentiation / physiology
  • Circadian Rhythm / physiology
  • Computer Simulation
  • Gene Regulatory Networks / physiology
  • Glass / chemistry
  • Hematopoietic Stem Cells / physiology
  • Markov Chains
  • Models, Theoretical*
  • Nonlinear Dynamics
  • Periodicity
  • RNA, Messenger / metabolism

Substances

  • RNA, Messenger