Data-Driven Superstabilization of Linear Systems under Quantization

TL;DR

This paper introduces a data-driven method for superstabilizing linear systems affected by quantization, using infinite-dimensional and exponential linear programs to ensure robust stabilization across all consistent system models.

Contribution

It develops a novel nonconservative approach leveraging sector-bounded uncertainty and exponential linear programs for superstabilization under quantization effects.

Findings

Successfully stabilizes example quantized systems

Enforces superstabilization across all consistent models

Uses exponential linear programs for efficient computation

Abstract

This paper focuses on the stabilization and regulation of linear systems affected by quantization in state-transition data and actuated input. The observed data are composed of tuples of current state, input, and the next state's interval ranges based on sensor quantization. Using an established characterization of input-logarithmically-quantized stabilization based on robustness to sector-bounded uncertainty, we formulate a nonconservative infinite-dimensional linear program that enforces superstabilization of all possible consistent systems under assumed priors. We solve this problem by posing a pair of exponentially-scaling linear programs, and demonstrate the success of our method on example quantized systems.