A fast sampling method for estimating the domain of attraction

Esmaeil Najafi; R. Babuska; G.A. Delgado Lopes

doi:10.1007/s11071-016-2926-7

A fast sampling method for estimating the domain of attraction

Esmaeil Najafi^*, R. Babuska, G.A. Delgado Lopes

^*Corresponding author for this work

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

43 Citations (Scopus)

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Abstract

Most stabilizing controllers designed for nonlinear systems are valid only within a specific region of the state space, called the domain of attraction (DoA). Computation of the DoA is usually costly and time-consuming. This paper proposes a computationally effective sampling approach to estimate the DoAs of nonlinear systems in real time. This method is validated to approximate the DoAs of stable equilibria in several nonlinear systems. In addition, it is implemented for the passivity-based learning controller designed for a second-order dynamical system. Simulation and experimental results show that, in all cases studied, the proposed sampling technique quickly estimates the DoAs, corroborating its suitability for real-time applications.

Original language	English
Pages (from-to)	823-834
Journal	Nonlinear Dynamics: an international journal of nonlinear dynamics and chaos in engineering systems
Volume	86
Issue number	2
DOIs	https://doi.org/10.1007/s11071-016-2926-7
Publication status	Published - 2016

Keywords

Domain of attraction
Lyapunov function
Optimization
Sampling method

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10.1007/s11071-016-2926-7

art_10.1007_s11071-016-2926-7Final published version, 2.17 MBLicence: CC BY

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AU - Delgado Lopes, G.A.

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AB - Most stabilizing controllers designed for nonlinear systems are valid only within a specific region of the state space, called the domain of attraction (DoA). Computation of the DoA is usually costly and time-consuming. This paper proposes a computationally effective sampling approach to estimate the DoAs of nonlinear systems in real time. This method is validated to approximate the DoAs of stable equilibria in several nonlinear systems. In addition, it is implemented for the passivity-based learning controller designed for a second-order dynamical system. Simulation and experimental results show that, in all cases studied, the proposed sampling technique quickly estimates the DoAs, corroborating its suitability for real-time applications.

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KW - Lyapunov function

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A fast sampling method for estimating the domain of attraction

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Keywords

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