TY - JOUR
T1 - Detection meeting control
T2 - Unstable steady states in high-dimensional nonlinear dynamical systems
AU - Ma, Huanfei
AU - Ho, Daniel W C
AU - Lai, Ying-Cheng
AU - Lin, Wei
N1 - Publisher Copyright:
© 2015 American Physical Society.
PY - 2015/10/2
Y1 - 2015/10/2
N2 - 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.
AB - 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.
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U2 - 10.1103/PhysRevE.92.042902
DO - 10.1103/PhysRevE.92.042902
M3 - Article
C2 - 26565299
AN - SCOPUS:84945217489
SN - 1539-3755
VL - 92
JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
IS - 4
M1 - 042902
ER -