Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Experiment Videos

Control of implicit chaotic maps using nonlinear approximations.

D. L. Hill1

  • 1Department of Mathematics and Statistics, University of Western Australia, Perth, WA, Australia.

Chaos (Woodbury, N.Y.)
|June 5, 2003
PubMed
Summary
This summary is machine-generated.

Related Concept Videos

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same journal

Topological dependence of viral mutation spread in complex host-interaction networks.

Chaos (Woodbury, N.Y.)·2026
Same journal

Multifractal signatures of Hamiltonian chaos in Hyperion's rotational dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

Exploring mechanisms for reversal of flow in tunicate hearts.

Chaos (Woodbury, N.Y.)·2026
Same journal

State estimation in spatiotemporal chaos via low-rank StatFEM.

Chaos (Woodbury, N.Y.)·2026
Same journal

Universal response functions in driven dissipative tunneling dynamics.

Chaos (Woodbury, N.Y.)·2026
Same journal

A network-based approach to characterize the dynamics of the coupling field of thermoacoustic oscillators in annular geometry.

Chaos (Woodbury, N.Y.)·2026
See all related articles

This study extends nonlinear control design for chaotic systems to implicit maps, successfully controlling the bouncing ball system without approximations. This advances chaos control methods for complex dynamics.

Area of Science:

  • Nonlinear Dynamics and Control Theory
  • Chaos Theory and Engineering Applications

Background:

  • Existing nonlinear approximation techniques for chaotic system control by Yagasaki and Uozumi.
  • Limitations of current methods when dealing with chaotic systems described by implicit maps.

Purpose of the Study:

  • To extend the Yagasaki-Uozumi nonlinear approximation technique for controller design.
  • To enable controller design for chaotic dynamical systems represented by implicit maps.
  • To apply the extended technique to control the bouncing ball system.

Main Methods:

  • Extension of nonlinear approximation methods for controller design.
  • Application to chaotic systems described by implicit maps.
  • Control of the bouncing ball system without the high-bounce approximation.

Related Experiment Videos

Main Results:

  • Successful extension of the nonlinear approximation technique to implicit maps.
  • Demonstration of effective control of the bouncing ball system using the new method.
  • Elimination of the need for the high-bounce approximation in controlling the bouncing ball system.

Conclusions:

  • The extended nonlinear approximation technique is effective for controlling chaotic systems with implicit maps.
  • This approach provides a viable method for controlling complex systems like the bouncing ball.
  • The findings expand the applicability of nonlinear control design for chaotic dynamical systems.