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Published on: September 11, 2019
Conditions of parameter identification from time series
Haipeng Peng1, Lixiang Li, Yixian Yang
1Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, P.O. Box 145, Beijing 100876, China.
Summary
This study identifies parameters in dynamical systems using synchronization. We reveal flaws in prior research and establish Gram matrix rank conditions for accurate parameter identification, even with noise.
Area of Science:
- Dynamical Systems and Control Theory
- Nonlinear Dynamics
- Signal Processing
Background:
- Parameter identification is crucial for understanding and controlling dynamical systems.
- Existing synchronization-based methods may have limitations or inaccuracies.
- Time series data is a common source for system analysis.
Purpose of the Study:
- To critically evaluate and correct recent findings on synchronization-based parameter identification.
- To establish robust theoretical conditions for accurate parameter estimation.
- To investigate the impact of noise on parameter identification and propose mitigation strategies.
Main Methods:
- Theoretical analysis of dynamical systems.
- Numerical simulations and examples.
- Investigation of Gram matrix properties (full rank conditions).
- Application of a mean filter to mitigate noise effects.
Main Results:
- Identified inaccuracies in previous synchronization-based parameter identification research.
- Established sufficient conditions (long-time and finite-time full rank) for Gram matrix-based parameter identification.
- Demonstrated the influence of additive noise on parameter estimation.
- Showcased the effectiveness of a mean filter in reducing noise-induced estimation fluctuations.
Conclusions:
- The proposed Gram matrix rank conditions provide a reliable basis for parameter identification.
- Synchronization-based methods require careful theoretical validation.
- Noise mitigation techniques are essential for practical applications of parameter identification.
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