title: Detection meeting control: Unstable steady states in high-dimensional nonlinear dynamical systems.
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.
authors.affiliation: School of Mathematical Sciences, Soochow University, Suzhou 215006, China.|Center for Computational Systems Biology, Fudan University, Shanghai 200433, China.
authors.forename: Huanfei
authors.initials: H
authors.lastname: Ma
authors.affiliation: Department of Mathematics, City University of Hong Kong, Hongkong, China.
authors.forename: Daniel W C
authors.initials: DW
authors.lastname: Ho
authors.affiliation: School of Electrical, Computer, and Energy Engineering, Arizona State University, Tempe, Arizona 85287-5706, USA.
authors.forename: Ying-Cheng
authors.initials: YC
authors.lastname: Lai
authors.affiliation: Center for Computational Systems Biology, Fudan University, Shanghai 200433, China.|School of Mathematical Sciences and SCMS, Fudan University, Shanghai 200433, China.
authors.forename: Wei
authors.initials: W
authors.lastname: Lin
mesh_terms: D000818:Animals; D002454:Cell Differentiation / Q000502:physiology; D002940:Circadian Rhythm / Q000502:physiology; D003198:Computer Simulation; D053263:Gene Regulatory Networks / Q000502:physiology; D005898:Glass / Q000737:chemistry; D006412:Hematopoietic Stem Cells / Q000502:physiology; D008390:Markov Chains; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D010507:Periodicity; D012333:RNA, Messenger / Q000378:metabolism
chemical_list: D012333:RNA, Messenger