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Derivative free data-driven stabilization of continuous-time linear systems from input-output data

Corrado Possieri

TL;DR

This work addresses stabilizing continuous-time LTI systems from input-output data without relying on time-derivative measurements. It introduces a filtering-based, derivative-free parameterization of the plant and couples it with an LMI-based output-feedback synthesis to compute stabilizing gains for both SISO and a class of MIMO systems. The main contributions include rigorous data-informativity conditions, a rank/recurrence framework, and practical LMI constructions that yield stabilizing controllers directly from IO data. The approach enables stable closed-loop behavior in a setting where explicit model identification is avoided, with potential robustness to measurement and input noise and clear paths for extending to order estimation and broader MIMO relaxations.

Abstract

This letter presents a data-driven framework for the design of stabilizing controllers from input-output data in the continuous-time, linear, and time-invariant domain. Rather than relying on measurements or reliable estimates of input and output time derivatives, the proposed approach uses filters to derive a parameterization of the system dynamics. This parameterization is amenable to the application of linear matrix inequalities enabling the design of stabilizing output feedback controllers from input-output data and the knowledge of the order of the system.

Derivative free data-driven stabilization of continuous-time linear systems from input-output data

TL;DR

This work addresses stabilizing continuous-time LTI systems from input-output data without relying on time-derivative measurements. It introduces a filtering-based, derivative-free parameterization of the plant and couples it with an LMI-based output-feedback synthesis to compute stabilizing gains for both SISO and a class of MIMO systems. The main contributions include rigorous data-informativity conditions, a rank/recurrence framework, and practical LMI constructions that yield stabilizing controllers directly from IO data. The approach enables stable closed-loop behavior in a setting where explicit model identification is avoided, with potential robustness to measurement and input noise and clear paths for extending to order estimation and broader MIMO relaxations.

Abstract

This letter presents a data-driven framework for the design of stabilizing controllers from input-output data in the continuous-time, linear, and time-invariant domain. Rather than relying on measurements or reliable estimates of input and output time derivatives, the proposed approach uses filters to derive a parameterization of the system dynamics. This parameterization is amenable to the application of linear matrix inequalities enabling the design of stabilizing output feedback controllers from input-output data and the knowledge of the order of the system.
Paper Structure (14 sections, 6 theorems, 87 equations, 1 figure, 1 algorithm)

This paper contains 14 sections, 6 theorems, 87 equations, 1 figure, 1 algorithm.

Table of Contents

  1. Introduction
  2. The proposed data-driven approach for the synthesis of an output feedback controller
  3. The single-input single-output case
  4. Data-driven modeling with input--output data
  5. Data-driven synthesis of a stabilizing gain
  6. Extension to a class of multi-input multi-output systems
  7. Conclusions
  8. Proof of \ref{['lem:interconnection']}
  9. Proof of \ref{['lem:relation']}
  10. Proof of \ref{['lem:null']}
  11. Proof of \ref{['thm:pe']}
  12. Proof of \ref{['thm:interMIMO']}
  13. Proof of \ref{['lem:relationMIMO']}
  14. Proof of \ref{['thm:peMIMO']}

Key Result

Theorem 1

Let ass:coprime hold and consider the interconnection of systems eq:systemIO, eq:filtu, and eq:filty, whose dynamics are where $\eta(t) =\mathrm{col}( \zeta(t) , \mu(t) , x(t) )$, $\eta(t)\in\mathbb{R}^{3n}$, $\chi(t)=\mathrm{col}( \zeta(t) , \mu(t) )$, $\chi(t)\in\mathbb{R}^{2n}$, $C_{\mathrm{i}} =\left[\right]$, and By letting $x(0)=x_0$, the dynamics of $\chi(t)$ are given by the pair

Theorems & Definitions (10)

  • Remark 1
  • Theorem 1
  • Corollary 1
  • proof
  • Lemma 1
  • Lemma 2
  • Remark 2
  • Proposition 1
  • Theorem 2
  • Remark 3