TY - GEN
T1 - Decentralized Polya's algorithm for stability analysis of large-scale nonlinear systems
AU - Kamyar, Reza
AU - Peet, Matthew
PY - 2013
Y1 - 2013
N2 - 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.
AB - 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.
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U2 - 10.1109/CDC.2013.6760813
DO - 10.1109/CDC.2013.6760813
M3 - Conference contribution
AN - SCOPUS:84902338761
SN - 9781467357173
T3 - Proceedings of the IEEE Conference on Decision and Control
SP - 5858
EP - 5863
BT - 2013 IEEE 52nd Annual Conference on Decision and Control, CDC 2013
PB - Institute of Electrical and Electronics Engineers Inc.
T2 - 52nd IEEE Conference on Decision and Control, CDC 2013
Y2 - 10 December 2013 through 13 December 2013
ER -