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

2 Citations (Scopus)

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 publicationProceedings of the IEEE Conference on Decision and Control
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

Other

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

Fingerprint

Large-scale Systems
Decentralized
Nonlinear systems
Stability Analysis
Nonlinear Systems
Lyapunov Inequality
Local Asymptotic Stability
Central Path
Polynomial Vector Fields
Primal-dual
Asymptotic stability
Linear matrix inequalities
Hypercube
Stability Condition
Nonlinear Differential Equations
Matrix Inequality
Linear Inequalities
Computational complexity
Dynamical systems
Computational Complexity

ASJC Scopus subject areas

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

Cite this

Kamyar, R., & Peet, M. (2013). Decentralized Polya's algorithm for stability analysis of large-scale nonlinear systems. In Proceedings of the IEEE Conference on Decision and Control (pp. 5858-5863). [6760813] Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/CDC.2013.6760813

Decentralized Polya's algorithm for stability analysis of large-scale nonlinear systems. / Kamyar, Reza; Peet, Matthew.

Proceedings of the IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers Inc., 2013. p. 5858-5863 6760813.

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

Kamyar, R & Peet, M 2013, Decentralized Polya's algorithm for stability analysis of large-scale nonlinear systems. in Proceedings of the IEEE Conference on Decision and Control., 6760813, Institute of Electrical and Electronics Engineers Inc., pp. 5858-5863, 52nd IEEE Conference on Decision and Control, CDC 2013, Florence, Italy, 12/10/13. https://doi.org/10.1109/CDC.2013.6760813
Kamyar R, Peet M. Decentralized Polya's algorithm for stability analysis of large-scale nonlinear systems. In Proceedings of the IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers Inc. 2013. p. 5858-5863. 6760813 https://doi.org/10.1109/CDC.2013.6760813
Kamyar, Reza ; Peet, Matthew. / Decentralized Polya's algorithm for stability analysis of large-scale nonlinear systems. Proceedings of the IEEE Conference on Decision and Control. Institute of Electrical and Electronics Engineers Inc., 2013. pp. 5858-5863
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