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Data to Certificate: Guaranteed Cost Control with Quantization-Aware System Identification

Shahab Ataei, Dipankar Maity, Debdipta Goswami

TL;DR

This work addresses the impact of data quantization on data-driven identification of unknown discrete-time LTI systems and on subsequent robust control design. It derives a worst-case identification error bound that depends solely on quantized data and the quantization resolution, with the bound scaling as ρ ∝ ε and ε ∝ 2^{-b}, and then designs an LMI-based guaranteed-cost controller that remains stable for all identification errors within this bound. The main contributions are a norm-bound on the identification error and an LMI formulation that yields a state-feedback gain K ensuring finite worst-case cost for all admissible ΔG. The results, validated on two dynamical systems, demonstrate that higher quantization bit-depth yields exponentially tighter guarantees and improved regulation performance, supporting reliable cloud-assisted control for low-power platforms.

Abstract

Cloud-assisted system identification and control have emerged as practical solutions for low-power, resource-constrained control systems such as micro-UAVs. In a typical cloud-assisted setting, state and input data are transmitted from local agents to a central computer over low-bandwidth wireless links, leading to quantization. This paper investigates the impact of state and input data quantization on a linear time invariant (LTI) system identification, derives a worst-case bound on the identification error, and develops a robust controller for guaranteed cost control. We establish a fundamental bound on the model error that depends only on the quantized data and quantization resolution, and develop a linear matrix inequality (LMI) based guaranteed cost robust controller under this error bound.

Data to Certificate: Guaranteed Cost Control with Quantization-Aware System Identification

TL;DR

This work addresses the impact of data quantization on data-driven identification of unknown discrete-time LTI systems and on subsequent robust control design. It derives a worst-case identification error bound that depends solely on quantized data and the quantization resolution, with the bound scaling as ρ ∝ ε and ε ∝ 2^{-b}, and then designs an LMI-based guaranteed-cost controller that remains stable for all identification errors within this bound. The main contributions are a norm-bound on the identification error and an LMI formulation that yields a state-feedback gain K ensuring finite worst-case cost for all admissible ΔG. The results, validated on two dynamical systems, demonstrate that higher quantization bit-depth yields exponentially tighter guarantees and improved regulation performance, supporting reliable cloud-assisted control for low-power platforms.

Abstract

Cloud-assisted system identification and control have emerged as practical solutions for low-power, resource-constrained control systems such as micro-UAVs. In a typical cloud-assisted setting, state and input data are transmitted from local agents to a central computer over low-bandwidth wireless links, leading to quantization. This paper investigates the impact of state and input data quantization on a linear time invariant (LTI) system identification, derives a worst-case bound on the identification error, and develops a robust controller for guaranteed cost control. We establish a fundamental bound on the model error that depends only on the quantized data and quantization resolution, and develop a linear matrix inequality (LMI) based guaranteed cost robust controller under this error bound.
Paper Structure (9 sections, 2 theorems, 45 equations, 3 figures)

This paper contains 9 sections, 2 theorems, 45 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. System Identification
  4. Effects of Quantization on $(\hat{A}, \hat{B})$
  5. Guaranteed Cost Controller under Identification Error
  6. Numerical Examples
  7. DC Motor with Load
  8. Mass Spring Damper
  9. Conclusions

Key Result

Theorem 1

If the following condition holds: then we can bound the system uncertainty matrices $\Delta G = [\Delta A, \Delta B]$ as follows: where

Figures (3)

  • Figure 1: Framework Overview.
  • Figure 2: Error and phase-portrait profile for DC Motor with Load: (a) relative error in matrix $A$; (b) relative error in matrix $B$; (c) uncertainty norm bound $\rho$; (d) finite-horizon cost and infinite-horizon cost bound; (e)--(h) phase portrait from regulation (with models identified from data snapshots generated by 50 independent random input and initial condition realization) for world-lengths $b=8,\ 10, \ 12,$ and $14$, respectively.
  • Figure 3: Error and phase-portrait profile for mass-spring-damper: (a) relative error in matrix $A$; (b) relative error in matrix $B$; (c) uncertainty norm bound $\rho$; (d) finite-horizon cost and infinite-horizon cost bound; (e)--(h) phase portrait from regulation (with models identified from data snapshots generated by 50 independent random input and initial condition realization) for world-lengths $b=8,\ 10,\ 12,$ and $14$, respectively.

Theorems & Definitions (4)

  • Theorem 1: Norm bounded uncertainty
  • proof
  • Theorem 2
  • proof