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Data-Driven Existence and Design of Target Output Controllers

Yuan Zhang, Wenxuan Xu, Mohamed Darouach, Tyrone Fernando

TL;DR

The paper tackles the problem of regulating target outputs in systems with unknown dynamics by developing data-driven existence conditions and direct design methods for target output controllers. It introduces rank-based criteria using only input and partial state data, enabling standard and augmented target output controllers without identifying $(A,B,F)$, and it proves a separation principle allowing independent design of observers and target controllers. A practical data-driven scheme for minimum-order augmentation and explicit pole-placement is provided, along with observer-based implementations that preserve the separation. Numerical examples validate the approach, showing effective stabilization and zero-regulation of target outputs under partial observability. This work advances scalable regulation of targeted state components in high-dimensional or partially observed systems by removing reliance on full-state controllability or accurate system models.

Abstract

Target output controllers aim at regulating a system's target outputs by placing poles of a suitable subsystem using partial state feedback, where full state controllability is not required. This paper establishes existence conditions for such controllers using input and partial state data, where the system dynamics are unknown. The approach bypasses traditional system identification steps and leverages the intrinsic structure of historical data to certify controller existence and synthesize a suitable feedback gain. Analytical characterizations are provided, ensuring that the resulting closed-loop system satisfies desired performance objectives such as pole placement or stabilization. Data-driven algorithms are then proposed to design target output controllers directly from data without identifying system parameters, where controllers with the order matching the number of target outputs and with minimum-order augmented target outputs are both addressed. Furthermore, a separation principle is revealed, decoupling the design of target output controllers from state observers. This enables the development of data-driven observer-based controllers that integrate estimation and control. Numerical examples validate the theoretical results and demonstrate the efficacy of the proposed approach.

Data-Driven Existence and Design of Target Output Controllers

TL;DR

The paper tackles the problem of regulating target outputs in systems with unknown dynamics by developing data-driven existence conditions and direct design methods for target output controllers. It introduces rank-based criteria using only input and partial state data, enabling standard and augmented target output controllers without identifying , and it proves a separation principle allowing independent design of observers and target controllers. A practical data-driven scheme for minimum-order augmentation and explicit pole-placement is provided, along with observer-based implementations that preserve the separation. Numerical examples validate the approach, showing effective stabilization and zero-regulation of target outputs under partial observability. This work advances scalable regulation of targeted state components in high-dimensional or partially observed systems by removing reliance on full-state controllability or accurate system models.

Abstract

Target output controllers aim at regulating a system's target outputs by placing poles of a suitable subsystem using partial state feedback, where full state controllability is not required. This paper establishes existence conditions for such controllers using input and partial state data, where the system dynamics are unknown. The approach bypasses traditional system identification steps and leverages the intrinsic structure of historical data to certify controller existence and synthesize a suitable feedback gain. Analytical characterizations are provided, ensuring that the resulting closed-loop system satisfies desired performance objectives such as pole placement or stabilization. Data-driven algorithms are then proposed to design target output controllers directly from data without identifying system parameters, where controllers with the order matching the number of target outputs and with minimum-order augmented target outputs are both addressed. Furthermore, a separation principle is revealed, decoupling the design of target output controllers from state observers. This enables the development of data-driven observer-based controllers that integrate estimation and control. Numerical examples validate the theoretical results and demonstrate the efficacy of the proposed approach.

Paper Structure

This paper contains 9 sections, 14 theorems, 61 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Data-driven existence and design of $r$-order target output controllers
  4. Data Matrices
  5. Existence and Design of $r$-Order Target Output Controllers
  6. Controller design by target augmentation
  7. Observer-based target output controllers
  8. Numerical simulations
  9. Conclusion

Key Result

Theorem 1

fernando2025existence The control law $u(t)=K F x(t)$, $K\in {\mathbb R}^{m\times r}$, is a $r$-order target output controller of system sys1 if and only if the following two conditions hold Moreover, when the above conditions hold, the poles of the target output controllers' are

Figures (2)

  • Figure 1: Responses of target outputs for Case 1.
  • Figure 2: Responses of the target output controller in Case 2.

Theorems & Definitions (20)

  • Definition 1: Target Output Controller, fernando2025existence
  • Theorem 1
  • Lemma 1
  • Definition 2
  • Remark 1
  • Lemma 2
  • Theorem 2: Data-Driven Existence Condition
  • Corollary 1
  • Remark 2
  • Corollary 2
  • ...and 10 more