On Goursat Normal Forms, Prolongations, and Control Systems

Abstract

The paper presents the method of exterior differential systems for analyzing nonlinear systems. The Goursat normal form is presented, and conditions are given for converting Pfaffian systems into this normal form. We give new conditions for converting Pfaffian systems into Goursat form after prolongation, and for linearizing control systems using dynamic extension. Several examples of mobile robots are examined, and it is shown that for some kinematic arrangements, a prolongation corresponding to a dynamic state feedback is needed to transform the corresponding Pfaffian system into Goursat form.

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Document Details

Document Type
Technical Report
Publication Date
Mar 16, 1994
Accession Number
ADA344171

Entities

People

  • D. Tilbury
  • S. Sastry

Organizations

  • University of California, Berkeley

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Communities of Interest

  • C4I

DTIC Thesaurus Topics

  • Algebra
  • Control Systems
  • Conversion
  • Coordinate Systems
  • Differential Equations
  • Electrical Engineering
  • Engineering
  • Equations
  • Feedback
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  • Language
  • Linear Systems
  • Nonlinear Systems
  • Partial Differential Equations
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Fields of Study

  • Computer science

Readers

  • Calculus or Mathematical Analysis
  • Graph Algorithms and Convex Optimization.
  • Robotics and Automation.

Technology Areas

  • AI & ML
  • AI & ML - Autonomous Systems
  • AI & ML - Bayesian Inference
  • Autonomy