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Estimation of non-symmetric and unbounded region of attraction using shifted shape function and R-composition
Dongyang Li1, Dmitry Ignatyev2, Antonios Tsourdos2
1School of Energy and Power Engineering, Nanjing University of Science and Technology, Nanjing 210094, China; School of Aerospace, Transport and Manufacturing, Cranfield University, Cranfield MK43 OAL, UK.
ISA Transactions
|December 12, 2022
Summary
This study introduces a novel method for estimating the region of attraction (ROA) of nonlinear systems. The approach enhances accuracy for complex, non-symmetric regions without increasing computational load.
Area of Science:
- Control Theory
- Nonlinear Systems Analysis
- Optimization
Background:
- Sum-of-squares programming is a standard technique for estimating the region of attraction (ROA) of stable equilibrium points in nonlinear polynomial systems.
- Current methods often produce conservative ROA estimates, particularly for systems with non-symmetric or unbounded regions of attraction.
- A need exists for more accurate and computationally efficient ROA estimation techniques.
Purpose of the Study:
- To develop a cost-effective and accurate method for estimating the region of attraction (ROA) of nonlinear polynomial systems.
- To overcome the limitations of existing sum-of-squares programming approaches, especially for non-symmetric and unbounded ROA.
- To improve the precision of ROA estimations without a significant increase in computational complexity.
Main Methods:
- The proposed method leverages Lyapunov theory and novel shape functions for ROA estimation.
- It iteratively positions the center of a shifted shape function (SSF) near the boundary of identified invariant subsets.
- Robust ROA subsets are generated using a collection of SSFs, with R-composition used to form a unified, richer level set.
Main Results:
- The proposed method demonstrates significant improvements in ROA estimation accuracy compared to existing techniques.
- Effectiveness is particularly notable for non-symmetric and unbounded regions of attraction.
- The approach maintains computational efficiency, avoiding substantial increases in processing time.
Conclusions:
- The developed method offers a more accurate and efficient approach to ROA estimation for nonlinear polynomial systems.
- It effectively addresses the conservatism associated with traditional sum-of-squares methods for complex ROA shapes.
- This technique provides a valuable tool for analyzing the stability of dynamical systems, especially in challenging non-symmetric or unbounded scenarios.
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