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Persistence of Excitation for Identifying Switched Linear Systems.

Biqiang Mu1, Tianshi Chen2, Changming Cheng3

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Summary

This study introduces a weaker condition for parameter uniqueness in switched linear systems. This new condition requires fewer data samples, improving efficiency in parameter estimation.

Keywords:
Persistence of excitationSwitched linear systems

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Area of Science:

  • Control Systems Engineering
  • System Identification
  • Signal Processing

Background:

  • Switched linear systems are crucial in modern control applications.
  • Parameter uniqueness is essential for accurate system modeling and control.
  • Existing methods for parameter identification often require extensive data.

Purpose of the Study:

  • To investigate parameter uniqueness in switched linear systems using persistence of excitation.
  • To develop a novel, less restrictive sufficient condition for persistent excitation.
  • To reduce the data sample requirements for parameter identification.

Main Methods:

  • Analysis of switched linear systems dynamics.
  • Application of persistence of excitation criteria.
  • Derivation of novel sufficient conditions for regressor properties.

Main Results:

  • A significantly weaker sufficient condition for persistent excitation is established.
  • This condition guarantees the uniqueness of parameter sets for switched linear systems.
  • The derived condition necessitates fewer samples compared to prior literature.

Conclusions:

  • The proposed condition offers a more efficient approach to parameter identification.
  • This work provides deeper insights into the relationships between subsystems.
  • The findings have implications for real-time system identification and adaptive control.