Adaptive-feedback control algorithm. (English) Zbl 1244.93064

Summary: This paper is motivated by giving the detailed proofs and some interesting remarks on the results the author obtained in a series of papers, where an adaptive-feedback algorithm was proposed to effectively stabilize and synchronize chaotic systems. This note proves in detail the strictness of this algorithm from the viewpoint of mathematics, and gives some interesting remarks for its potential applications to chaos control and synchronization. In addition, a significant comment on synchronization-based parameter estimation is given, which shows some techniques proposed in literature less strict and ineffective in some cases.


93B52 Feedback control
93C40 Adaptive control/observation systems
34H10 Chaos control for problems involving ordinary differential equations
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
Full Text: DOI


[1] DOI: 10.1103/PhysRevLett.64.1196 · Zbl 0964.37501
[2] DOI: 10.1103/PhysRevLett.64.821 · Zbl 0938.37019
[3] DOI: 10.1016/S0370-1573(99)00096-4
[4] DOI: 10.1016/S0370-1573(02)00137-0 · Zbl 0995.37022
[5] DOI: 10.1103/PhysRevLett.93.214101
[6] DOI: 10.1103/PhysRevE.71.037203
[7] DOI: 10.1103/PhysRevE.69.067201
[8] J. P. Lasalle, IRE Trans. Circuit Theory 7 pp 520– (1960) ISSN: http://id.crossref.org/issn/0096-2007
[9] DOI: 10.1103/PhysRevE.50.R647
[10] DOI: 10.1103/PhysRevLett.76.1232
[11] DOI: 10.1063/1.1635095 · Zbl 1080.37092
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.