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A DREM-Based Approach for the Identification of Chaotic Systems
Carlos Aguilar-Ibanez1, Miguel S Suarez-Castanon2, Belem Saldivar3
1Centro de Investigacion en Computacion, Instituto Politecnico Nacional, Ciudad de Mexico 07738, Mexico.
Entropy (Basel, Switzerland)
|September 27, 2025
Summary
This study introduces a novel least-squares method to identify chaotic systems. The technique transforms nonlinear systems into a linear regression, enabling parameter recovery and enhancing chaos analysis.
Area of Science:
- Control Theory
- Nonlinear Dynamics
- Systems Identification
Background:
- Chaotic systems present significant challenges in modeling and identification.
- Existing methods often struggle with the inherent nonlinearities and complexities of chaotic dynamics.
Purpose of the Study:
- To develop a straightforward methodology for identifying specific classes of chaotic systems.
- To leverage algebraic observability and identifiability for system analysis.
Main Methods:
- A novel least-squares approach is applied to chaotic systems.
- The system output and its derivatives are used to transform the system into a chain of integrators.
- A high-gain observer estimates system states and nonlinear terms.
- The transformed system is represented as a linear regression equation.
Main Results:
- The methodology successfully identifies parameters of chaotic systems.
- The approach effectively handles nonlinearities by lumping them into an estimable term.
- The least-squares method is enabled by rewriting the system in a linear regression form.
Conclusions:
- The proposed method offers an effective way to identify chaotic system parameters.
- This technique simplifies the analysis of complex nonlinear dynamics.
- The approach is suitable for algebraically observable and identifiable chaotic systems.
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