Lyapunov-Based Feedback Control of Border Collision Bifurcations in Piecewise Smooth Systems

Abstract

Feedback control of piecewise smooth discrete time systems that undergo border collision bifurcations is considered. These bifurcations occur when a fixed point or a periodic orbit of a piecewise smooth system crosses or collides with the border between two regions of smooth operation as a system parameter is quasi-statically varied. The goal of the control effort in this work is to modify the bifurcation so that the bifurcated steady state is locally attracting and locally unique. To achieve this, Lyapunov-based techniques are used. A sufficient condition for nonbifurcation with persistent stability in piecewise smooth maps of dimension n that depend on a parameter is derived. The derived condition is in terms of linear matrix inequalities. This condition is then used as a basis for the design of feedback controls to eliminate border collision bifurcations in piecewise smooth maps and to produce desirable behavior.

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Document Details

Document Type
Technical Report
Publication Date
Jan 01, 2004
Accession Number
ADA439520

Entities

People

  • Eyad H. Abed
  • Munther A. Hassouneh

Organizations

  • University of Maryland

Tags

Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Classification
  • Closed Loop Systems
  • Collisions
  • Continuity
  • Coordinate Systems
  • Dynamics
  • Eigenvalues
  • Engineering
  • Feedback
  • Inequalities
  • Linear Systems
  • Lyapunov Functions
  • Military Research
  • Open Loop Systems
  • Switching
  • Trajectories
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Finite Element Method (FEM) for solving Partial Differential Equations (PDEs)
  • Robotics and Automation.

Technology Areas

  • Space
  • Space - Spacecraft Maneuvers