A Decomposition Technique for Nonlinear Dynamical System Analysis

Author

Anderson, Jon ; Papachristodoulou, A.

Author_Institution

Dept. of Eng. Sci., Univ. of Oxford, Oxford, UK

Volume

57

Issue

6

fYear

2012

fDate

6/1/2012 12:00:00 AM

Firstpage

1516

Lastpage

1521

Abstract

A method for analyzing large-scale nonlinear dynamical systems by decomposing them into coupled lower order subsystems that are sufficiently simple for computational analysis is presented. It is shown that the decomposition approach can be used to scale the Sum of Squares programming framework for nonlinear systems analysis. The method constructs subsystem Lyapunov functions which are used to form a composite Lyapunov function for the whole system. Further computational savings are achieved if a method based on sparsity maximization is used to obtain the subsystem Lyapunov functions.

Keywords

Lyapunov methods; control system analysis; large-scale systems; nonlinear control systems; nonlinear dynamical systems; composite Lyapunov function; computational analysis; coupled lower order subsystems; decomposition technique; large-scale nonlinear dynamical system analysis method; sparsity maximization; subsystem Lyapunov functions; sum of squares programming framework; Heuristic algorithms; Lyapunov methods; Matrix decomposition; Partitioning algorithms; Polynomials; Stability analysis; Vectors; Large-scale systems; nonlinear systems; sum of squares (SOS);

fLanguage

English

Journal_Title

Automatic Control, IEEE Transactions on

Publisher

ieee

ISSN

0018-9286

Type

jour

DOI

10.1109/TAC.2011.2175058

Filename

6070953