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Data-Driven Superstabilization of Linear Systems under Quantization.

Jared Miller1,2, Jian Zheng2, Mario Sznaier2

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View abstract on PubMed

Summary
This summary is machine-generated.

This study addresses stabilizing linear systems with quantized data. A novel linear programming approach ensures system stability despite sensor and input quantization, demonstrating effectiveness on example systems.

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Area of Science:

  • Control Systems Engineering
  • Information Theory
  • Applied Mathematics

Background:

  • Linear systems are susceptible to performance degradation due to data quantization.
  • Quantization in state-transition data and control inputs poses significant challenges for system stabilization.
  • Existing methods often struggle with non-conservative stabilization under quantization.

Purpose of the Study:

  • To develop a robust method for stabilizing linear systems with quantized state-transition data and control inputs.
  • To formulate a nonconservative approach that accounts for sensor quantization and input limitations.
  • To ensure superstabilization for all systems consistent with observed quantized data.

Main Methods:

  • Utilizing a characterization of input-logarithmically-quantized stabilization based on robustness to sector-bounded uncertainty.
  • Formulating a nonconservative infinite-dimensional linear program.
  • Solving the problem via a pair of exponentially-scaling linear programs.

    • Main Results:

    • The proposed method successfully enforces superstabilization for quantized linear systems.
    • The infinite-dimensional linear program provides a nonconservative solution.
    • Demonstrated effectiveness on various example quantized systems.

    Conclusions:

    • The developed linear programming technique offers a powerful tool for stabilizing quantized systems.
    • This approach enhances control system reliability in the presence of data uncertainty.
    • The method advances the field of robust control for systems with digital components.