Decentralized Polya's algorithm for stability analysis of large-scale nonlinear systems

Reza Kamyar, Matthew Peet

Research output: Chapter in Book/Report/Conference proceedingConference contribution

3 Scopus citations

Abstract

In this paper, we introduce an algorithm to decentralize the computation associated with the stability analysis of systems of nonlinear differential equations with a large number of states. The algorithm applies to dynamical systems with polynomial vector fields and checks the local asymptotic stability on hypercubes. We perform the analysis in three steps. First, by applying a multi-simplex version of Polya's theorem to some Lyapunov inequalities, we derive a sequence of stability conditions of increasing accuracy in the form of structured linear matrix inequalities. Then, we design a set-up algorithm to decentralize the computation of the coefficients of the LMIs, among the processing units of a parallel environment. Finally, we use a parallel primal-dual central path algorithm, specifically designed to solve the structured LMIs given by the set-up algorithm. For a sufficiently large number of available processors, the per-core computational complexity of the resulting algorithm is fixed with the accuracy. The algorithm demonstrates a near-linear speed-up in numerical experiments.

Original languageEnglish (US)
Title of host publication2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
PublisherInstitute of Electrical and Electronics Engineers Inc.
Pages5858-5863
Number of pages6
ISBN (Print)9781467357173
DOIs
StatePublished - 2013
Event52nd IEEE Conference on Decision and Control, CDC 2013 - Florence, Italy
Duration: Dec 10 2013Dec 13 2013

Publication series

NameProceedings of the IEEE Conference on Decision and Control
ISSN (Print)0191-2216

Other

Other52nd IEEE Conference on Decision and Control, CDC 2013
CountryItaly
CityFlorence
Period12/10/1312/13/13

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Modeling and Simulation
  • Control and Optimization

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