Decentralized computation for robust stability of large-scale systems with parameters on the hypercube

Reza Kamyar, Matthew M. Peet

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

4 Citations (Scopus)

Abstract

In this paper, we propose a parallel algorithm to solve the problem of robust stability of systems with large state-space and with large number of uncertain parameters. The dependence of the system on the parameters is polynomial and the parameters are assumed to lie in a hypercube. Although the parameters are assumed to be static, the method can also be applied to systems with time-varying parameters. The algorithm relies on a variant of Polya's theorem which is applicable to polynomials with variables inside a multi-simplex. The algorithm is divided into formulation and solution subroutines. In the formulation phase, we construct a large-scale semidefinite programming problem with structured elements. In the solution phase, we use a structured primal-dual approach to solve the structured semidefinite programming problem. In both subroutines, computation, memory and communication are efficiently distributed over hundreds and potentially thousands of processors. Numerical tests confirm the accuracy and scalability of the proposed algorithm.

Original languageEnglish (US)
Title of host publicationProceedings of the IEEE Conference on Decision and Control
Pages6259-6264
Number of pages6
DOIs
StatePublished - 2012
Event51st IEEE Conference on Decision and Control, CDC 2012 - Maui, HI, United States
Duration: Dec 10 2012Dec 13 2012

Other

Other51st IEEE Conference on Decision and Control, CDC 2012
CountryUnited States
CityMaui, HI
Period12/10/1212/13/12

Fingerprint

Robust Stability
Large-scale Systems
Hypercube
Decentralized
Large scale systems
Subroutines
Semidefinite Programming
Polynomials
Structured programming
Time-varying Parameters
Polynomial
Formulation
Uncertain Parameters
Primal-dual
Parallel algorithms
Parallel Algorithms
Scalability
State Space
Data storage equipment
Communication

ASJC Scopus subject areas

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

Cite this

Kamyar, R., & Peet, M. M. (2012). Decentralized computation for robust stability of large-scale systems with parameters on the hypercube. In Proceedings of the IEEE Conference on Decision and Control (pp. 6259-6264). [6425907] https://doi.org/10.1109/CDC.2012.6425907

Decentralized computation for robust stability of large-scale systems with parameters on the hypercube. / Kamyar, Reza; Peet, Matthew M.

Proceedings of the IEEE Conference on Decision and Control. 2012. p. 6259-6264 6425907.

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

Kamyar, R & Peet, MM 2012, Decentralized computation for robust stability of large-scale systems with parameters on the hypercube. in Proceedings of the IEEE Conference on Decision and Control., 6425907, pp. 6259-6264, 51st IEEE Conference on Decision and Control, CDC 2012, Maui, HI, United States, 12/10/12. https://doi.org/10.1109/CDC.2012.6425907
Kamyar R, Peet MM. Decentralized computation for robust stability of large-scale systems with parameters on the hypercube. In Proceedings of the IEEE Conference on Decision and Control. 2012. p. 6259-6264. 6425907 https://doi.org/10.1109/CDC.2012.6425907
Kamyar, Reza ; Peet, Matthew M. / Decentralized computation for robust stability of large-scale systems with parameters on the hypercube. Proceedings of the IEEE Conference on Decision and Control. 2012. pp. 6259-6264
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