Estimation of region of attraction for polynomial nonlinear systems: A numerical method

2014 ◽  
Vol 53 (1) ◽  
pp. 25-32 ◽  
Author(s):  
Larissa Khodadadi ◽  
Behzad Samadi ◽  
Hamid Khaloozadeh
Keyword(s):  
Nonlinear Systems ◽  
Numerical Method ◽  
Region Of Attraction

scholarly journals Nonlinear Systems of Volterra Equations with Piecewise Smooth Kernels: Numerical Solution and Application for Power Systems Operation

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1257 ◽  
Author(s):  
Denis Sidorov ◽  
Aleksandr Tynda ◽  
Ildar Muftahov ◽  
Aliona Dreglea ◽  
Fang Liu
Keyword(s):  
Nonlinear Systems ◽  
Power Systems ◽  
Numerical Method ◽  
Storage Systems ◽  
Piecewise Smooth ◽  
Volterra Equations ◽  
Dynamical Models ◽  
Smooth Kernels ◽  
Power Systems Operation ◽  
Real World Problems

The evolutionary integral dynamical models of storage systems are addressed. Such models are based on systems of weakly regular nonlinear Volterra integral equations with piecewise smooth kernels. These equations can have non-unique solutions that depend on free parameters. The objective of this paper was two-fold. First, the iterative numerical method based on the modified Newton–Kantorovich iterative process is proposed for a solution of the nonlinear systems of such weakly regular Volterra equations. Second, the proposed numerical method was tested both on synthetic examples and real world problems related to the dynamic analysis of microgrids with energy storage systems.

scholarly journals Exact Asymptotic Stability Analysis and Region-of-Attraction Estimation for Nonlinear Systems

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Min Wu ◽  
Zhengfeng Yang ◽  
Wang Lin
Keyword(s):  
Stability Analysis ◽  
Nonlinear Systems ◽  
Asymptotic Stability ◽  
Lyapunov Function ◽  
Lyapunov Functions ◽  
Nonlinear Dynamical Systems ◽  
Region Of Attraction ◽  
Nonlinear Dynamical ◽  
Recovery Techniques ◽  
Regions Of Attraction

We address the problem of asymptotic stability and region-of-attraction analysis of nonlinear dynamical systems. A hybrid symbolic-numeric method is presented to compute exact Lyapunov functions and exact estimates of regions of attraction of nonlinear systems efficiently. A numerical Lyapunov function and an estimate of region of attraction can be obtained by solving an (bilinear) SOS programming via BMI solver, then the modified Newton refinement and rational vector recovery techniques are applied to obtain exact Lyapunov functions and verified estimates of regions of attraction with rational coefficients. Experiments on some benchmarks are given to illustrate the efficiency of our algorithm.

Estimation of the regions of attraction for autonomous nonlinear systems

2018 ◽  
Vol 41 (1) ◽  
pp. 97-106
Author(s):  
Guoqiang Yuan ◽  
Yinghui Li
Keyword(s):  
Nonlinear Systems ◽  
Iterative Methods ◽  
Jacobi Equation ◽  
Time Dependent ◽  
Implicit Function ◽  
Region Of Attraction ◽  
Sublevel Set ◽  
Initial Domain ◽  
Regions Of Attraction ◽  
Hamilton Jacobi Equation

A methodology for estimating the region of attraction for autonomous nonlinear systems is developed. The methodology is based on a proof that the region of attraction can be estimated accurately by the zero sublevel set of an implicit function which is the viscosity solution of a time-dependent Hamilton–Jacobi equation. The methodology starts with a given initial domain and yields a sequence of region of attraction estimates by tracking the evolution of the implicit function. The resulting sequence is contained in and converges to the exact region of attraction. While alternative iterative methods for estimating the region of attraction have been proposed, the methodology proposed in this paper can compute the region of attraction to achieve any desired accuracy in a dimensionally independent and efficient way. An implementation of the proposed methodology has been developed in the Matlab environment. The correctness and efficiency of the methodology are verified through a few examples.

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