Development of Analysis Tools for Certification of Flight Control Laws

Abstract

We have improved our ability to analyze uncertain system dynamics, including nonaffine parametric uncertainty as well as unmodeled dynamics. This entailed polytopic covering methods for graphs of vector-valued polynomial functions, and local small-gain theorems. We use simulation as a key step in aiding the nonconvex search for proofs (Lyapunov functions) and proof certificates (multipliers). Some aspects of the calculation are trivially parallelizable, and we have employed a 9-machine cluster to speed-up the analysis of uncertain systems. We also began more detailed study of systems with marginally stable linearizations (ie., adaptive systems). Finally, we made precise our claim that these techniques represent a quantitative and definitive improvement over linearized analysis.

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Document Details

Document Type
Technical Report
Publication Date
Mar 31, 2009
Accession Number
ADA531629

Entities

People

  • Andrew Packard
  • Gary Balas
  • Pete Seiler

Organizations

  • University of California, Berkeley

Tags

Communities of Interest

  • Air Platforms
  • C4I
  • Human Systems
  • Space

DTIC Thesaurus Topics

  • Air Force
  • Algorithms
  • Computational Complexity
  • Computational Science
  • Coverings
  • Differential Equations
  • Engineers
  • Linear Programming
  • Linear Systems
  • Lyapunov Functions
  • Mechanical Engineering
  • Nonlinear Systems
  • Optimization
  • Real Variables
  • Semidefinite Programming
  • Simulations
  • Two Dimensional

Fields of Study

  • Mathematics

Readers

  • Adaptive Control and Estimation with Uncertainty in Dynamic Systems.
  • Operations Research
  • Systems Analysis and Design