Local stability analysis for large polynomial spline systems

Torbjørn Cunis; Jean Philippe Condomines; Laurent Burlion

doi:10.1016/j.automatica.2019.108773

Local stability analysis for large polynomial spline systems

Torbjørn Cunis, Jean Philippe Condomines, Laurent Burlion

School of Engineering, Mechanical & Aerospace Engineering

Research output: Contribution to journal › Article › peer-review

8 Scopus citations

Abstract

Polynomial switching systems such as multivariate splines provide accurate fitting while retaining an algebraic representation and offering arbitrary degrees of smoothness; yet, application of sum-of-squares techniques for local stability analysis is computationally demanding for a large number of subdomains. This communiqué presents an algorithm for region of attraction estimation that is confined to those subdomains actually covered by the estimate, thereby significantly reducing computation time. Correctness of the results is subsequently proven and the run time is approximated in terms of the number of total and covered subdomains. Application to longitudinal aircraft motion concludes the study.

Original language	English (US)
Article number	108773
Journal	Automatica
Volume	113
DOIs	https://doi.org/10.1016/j.automatica.2019.108773
State	Published - Mar 2020

All Science Journal Classification (ASJC) codes

Control and Systems Engineering
Electrical and Electronic Engineering

Keywords

Lyapunov function
Nonlinear analysis
Polynomial methods
Stability analysis
Switching functions

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10.1016/j.automatica.2019.108773

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title = "Local stability analysis for large polynomial spline systems",

abstract = "Polynomial switching systems such as multivariate splines provide accurate fitting while retaining an algebraic representation and offering arbitrary degrees of smoothness; yet, application of sum-of-squares techniques for local stability analysis is computationally demanding for a large number of subdomains. This communiqu{\'e} presents an algorithm for region of attraction estimation that is confined to those subdomains actually covered by the estimate, thereby significantly reducing computation time. Correctness of the results is subsequently proven and the run time is approximated in terms of the number of total and covered subdomains. Application to longitudinal aircraft motion concludes the study.",

keywords = "Lyapunov function, Nonlinear analysis, Polynomial methods, Stability analysis, Switching functions",

author = "Torbj{\o}rn Cunis and Condomines, {Jean Philippe} and Laurent Burlion",

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year = "2020",

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doi = "10.1016/j.automatica.2019.108773",

language = "English (US)",

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TY - JOUR

T1 - Local stability analysis for large polynomial spline systems

AU - Cunis, Torbjørn

AU - Condomines, Jean Philippe

AU - Burlion, Laurent

PY - 2020/3

Y1 - 2020/3

N2 - Polynomial switching systems such as multivariate splines provide accurate fitting while retaining an algebraic representation and offering arbitrary degrees of smoothness; yet, application of sum-of-squares techniques for local stability analysis is computationally demanding for a large number of subdomains. This communiqué presents an algorithm for region of attraction estimation that is confined to those subdomains actually covered by the estimate, thereby significantly reducing computation time. Correctness of the results is subsequently proven and the run time is approximated in terms of the number of total and covered subdomains. Application to longitudinal aircraft motion concludes the study.

AB - Polynomial switching systems such as multivariate splines provide accurate fitting while retaining an algebraic representation and offering arbitrary degrees of smoothness; yet, application of sum-of-squares techniques for local stability analysis is computationally demanding for a large number of subdomains. This communiqué presents an algorithm for region of attraction estimation that is confined to those subdomains actually covered by the estimate, thereby significantly reducing computation time. Correctness of the results is subsequently proven and the run time is approximated in terms of the number of total and covered subdomains. Application to longitudinal aircraft motion concludes the study.

KW - Lyapunov function

KW - Nonlinear analysis

KW - Polynomial methods

KW - Stability analysis

KW - Switching functions

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VL - 113

JO - Automatica

JF - Automatica

M1 - 108773

ER -

Local stability analysis for large polynomial spline systems

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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