Using SOS and sublevel set volume minimization for estimation of forward reachable sets

Morgan Jones, Matthew M. Peet

Research output: Contribution to journalConference article

Abstract

In this paper we propose a convex Sum-of-Squares optimization problem for finding outer approximations of forward reachable sets for nonlinear uncertain Ordinary Differential Equations (ODE’s) with either (or both) L2 or point-wise bounded input disturbances. To make our approximations tight we seek to minimize the volume of our approximation set. Our approach to volume minimization is based on the use of a convex determinant-like objective function. We provide several numerical examples including the Lorenz system and the Van der Pol oscillator.

Original languageEnglish (US)
Pages (from-to)484-489
Number of pages6
JournalIFAC-PapersOnLine
Volume52
Issue number16
DOIs
StatePublished - Sep 2019
Externally publishedYes
Event11th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2019 - Vienna, Austria
Duration: Sep 4 2019Sep 6 2019

Keywords

  • Convex optimization
  • Nonlinear analysis
  • Reachable states
  • Uncertainty

ASJC Scopus subject areas

  • Control and Systems Engineering

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