Estimating the Region of Attraction via collocation for autonomous nonlinear systems

2012 ◽  
Vol 41 (2) ◽  
pp. 263-284 ◽  
Author(s):  
M. Rezaiee-Pajand ◽  
B. Moghaddasie
Keyword(s):  
Nonlinear Systems ◽  
Region Of Attraction

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.

A Piecewise Approximation Approach to Nonlinear Systems: Stability and Region of Attraction

2015 ◽  
Vol 23 (6) ◽  
pp. 2231-2244 ◽  
Author(s):  
Stefan Gering ◽  
Luka Eciolaza ◽  
Jurgen Adamy ◽  
Michio Sugeno
Keyword(s):  
Nonlinear Systems ◽  
Region Of Attraction ◽  
Approximation Approach

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

A Stability Result With Application to Nonlinear Regulation1

2002 ◽  
Vol 124 (3) ◽  
pp. 452-456 ◽  
Author(s):  
Wilbur Langson ◽  
Andrew Alleyne
Keyword(s):  
Nonlinear Systems ◽  
Stability Result ◽  
Linear Representation ◽  
State Regulation ◽  
System Stability ◽  
Stability And Convergence ◽  
Region Of Attraction ◽  
Linear Quadratic ◽  
Local Asymptotic Stability ◽  
Lq Optimal Control

This work considers a class of nonlinear systems whose feedback controller is generated via the solution of a State Dependent Riccati Equation (SDRE) as proposed in Banks and Manha and Cloutier. A pseudo-linear representation of the class of nonlinear systems is described and a stability analysis is performed. This analysis leads to sufficiency conditions under which local asymptotic stability is present. These conditions allow for the computation of a Region of Attraction estimate for system stability. These results are then applied to study stability and convergence properties of closed loop systems that arise when the SDRE technique is used. Many of the benefits of Linear Quadratic (LQ) Optimal Control, such as a tradeoff between state regulation and input effort, are readily transparent in the nonlinear scheme. The tradeoff ability is the major advantage of the SDRE over several other nonlinear control schemes. The computed Region of Attraction, while sufficient, is demonstrated to also be quite conservative. An example is used to examine the SDRE approach.

scholarly journals Finite-Time Optimization Stabilization for a Class of Constrained Switched Nonlinear Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Baili Su ◽  
Dandan Chunyu
Keyword(s):  
Nonlinear Systems ◽  
Finite Time ◽  
Switched Nonlinear Systems ◽  
Region Of Attraction ◽  
Time Stability ◽  
Finite Time Stability ◽  
System A ◽  
Time Optimization ◽  
Switched Nonlinear System ◽  
And Control

This paper studies the finite-time stability problem of a class of switched nonlinear systems with state constraints and control constrains. For each subsystem, optimization controller is designed by choosing the appropriate Lyapunov function to stabilize the subsystem in finite time and the estimation of the region of attraction can be prescribed. For the whole switched nonlinear system, a suitable switched law is designed to ensure the following: (1) at the time of the transition, Lyapunov function’s value of the switched-in subsystem being less than the value of the last subsystem; (2) the finite-time stability of the whole close-loop system. Finally, a simulation example is used to verify the effectiveness of the proposed algorithm.

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