Invariance of Conjunctions of Polynomial Equalities for Algebraic Differential Equations

Abstract

In this paper we seek to provide greater automation for formal deductive verification tools working with continuous and hybrid dynamical systems. We present an efficient procedure to check invariance of conjunctions of polynomial equalities under the flow of polynomial ordinary differential equations. The procedure is based on a necessary and sufficient condition that characterizes invariant conjunctions of polynomial equalities. We contrast this approach to an alternative one which combines fast and sufficient (but not necessary) conditions using differential cuts for soundly restricting the system evolution domain.

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Document Details

Document Type
Technical Report
Publication Date
Jul 01, 2014
Accession Number
ADA622294

Entities

People

  • Andrew Sogokon
  • AndrĂ© Platzer
  • Khalil Ghorbal

Organizations

  • Carnegie Mellon University

Tags

Communities of Interest

  • Air Platforms
  • Energy and Power Technologies
  • Human Systems

DTIC Thesaurus Topics

  • Algorithms
  • Automation
  • Coefficients
  • Computational Complexity
  • Computer Science
  • Construction
  • Contrast
  • Differential Equations
  • Elimination
  • Equations
  • Hybrid Systems
  • Integrals
  • Invariance
  • Linear Differential Equations
  • Personal Information Managers
  • Polynomials
  • Verification

Fields of Study

  • Mathematics

Readers

  • Calculus or Mathematical Analysis
  • Mathematical Modeling and Probability Theory.