Stationary Bifurcation Control for Systems with Uncontrollable Linearization

Abstract

Stationary bifurcation control is studied under the assumption that the critical zero eigenvalue is uncontrollable for the linearized system. The development facilitates explicit construction of feedback control laws that render the bifurcation supercritical. Thus, the bifurcated equilibria in the controlled system are guaranteed stable. Both pitchfork bifurcation and transcritical bifurcation are addressed. The results obtained for pitchfork bifurcations apply to general nonlinear models smooth in the state and the control. For transcritical bifurcations, the results require the system to be affine in the control.

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Document Details

Document Type
Technical Report
Publication Date
Jan 28, 1999
Accession Number
ADA438515

Entities

People

  • Eyad H. Abed
  • Taihyun Kim

Organizations

  • University of Maryland

Tags

Communities of Interest

  • Air Platforms
  • C4I

DTIC Thesaurus Topics

  • Air Force
  • Autonomous Systems
  • Axial Flow
  • Axial Flow Compressors
  • Closed Loop Systems
  • Coefficients
  • Eigenvalues
  • Eigenvectors
  • Electrical Engineering
  • Engineering
  • Equations
  • Feedback
  • Nonlinear Systems
  • Open Loop Systems
  • Scientific Research
  • Stationary
  • Universities

Fields of Study

  • Biology
  • Mathematics

Readers

  • Fluid Dynamics.
  • Structural Dynamics.
  • Systems Analysis and Design