Data-Driven Superstabilization of Linear Systems under Quantization

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.