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Data-Driven Output-Based Approach to the Output Regulation Problem of Unknown Linear Systems via Value Iteration

Haoyan Lin, Jie Huang

TL;DR

The paper addresses output regulation for unknown linear systems by developing a data-driven, value-iteration framework. It introduces a novel output-feedback control law that avoids explicit dependence on the observer gain and reduces the problem to a state-feedback design for an augmented auxiliary system, enabling VI-based learning. A key contribution is the systematic VI-based method to solve the augmented-LQR problem with relaxed solvability conditions and reduced unknowns, plus a rigorous link between state- and output-feedback LQR in the augmented setting. Numerical examples demonstrate convergence and effective tracking for both E=0 and E≠0 scenarios, highlighting the approach's practicality for stabilizable-but-not-controllable plants in a model-free, data-driven setting.

Abstract

The output regulation problem for unknown linear systems has been studied using state-based and output-based internal model approaches in the special case with no disturbances. This paper further investigates the output regulation problem for unknown linear systems using a data-driven output-based approach via value iteration. For this purpose, we first develop a novel output-feedback control law that does not explicitly rely on the observer gain to solve the output regulation problem. We then show that the data-driven approach for designing an output-feedback control law for the given plant can be reduced to the data-driven design of a state-feedback control law for a well-defined augmented auxiliary system. As a result, we develop a systematic data-driven approach to solve the output regulation problem for unknown linear systems via value iteration. Finally, we establish a relation between the data-driven state-feedback control law and the data-driven output-feedback control law in the LQR sense.

Data-Driven Output-Based Approach to the Output Regulation Problem of Unknown Linear Systems via Value Iteration

TL;DR

The paper addresses output regulation for unknown linear systems by developing a data-driven, value-iteration framework. It introduces a novel output-feedback control law that avoids explicit dependence on the observer gain and reduces the problem to a state-feedback design for an augmented auxiliary system, enabling VI-based learning. A key contribution is the systematic VI-based method to solve the augmented-LQR problem with relaxed solvability conditions and reduced unknowns, plus a rigorous link between state- and output-feedback LQR in the augmented setting. Numerical examples demonstrate convergence and effective tracking for both E=0 and E≠0 scenarios, highlighting the approach's practicality for stabilizable-but-not-controllable plants in a model-free, data-driven setting.

Abstract

The output regulation problem for unknown linear systems has been studied using state-based and output-based internal model approaches in the special case with no disturbances. This paper further investigates the output regulation problem for unknown linear systems using a data-driven output-based approach via value iteration. For this purpose, we first develop a novel output-feedback control law that does not explicitly rely on the observer gain to solve the output regulation problem. We then show that the data-driven approach for designing an output-feedback control law for the given plant can be reduced to the data-driven design of a state-feedback control law for a well-defined augmented auxiliary system. As a result, we develop a systematic data-driven approach to solve the output regulation problem for unknown linear systems via value iteration. Finally, we establish a relation between the data-driven state-feedback control law and the data-driven output-feedback control law in the LQR sense.
Paper Structure (18 sections, 111 equations, 4 figures, 1 table, 6 algorithms)

This paper contains 18 sections, 111 equations, 4 figures, 1 table, 6 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries and Problem Formulation
  3. State-Based Value Iteration Approach for Solving LQR Problem without Knowing $A$, $B$ and $C$ Bian2016
  4. Output-Based Value Iteration Approach for Solving LQR Problem without Knowing $A$, $B$ and $C$Lin2024
  5. Output Regulation Problem by Parameterized Output-Feedback Control
  6. Existing Results
  7. Output Regulation Problem by Parameterized Output-Feedback Control
  8. Main Results
  9. Output-based Output Regulation Problem by Modified Internal Model Approach
  10. VI Method for Solving \ref{['AREMrho']}
  11. Improved VI Algorithm
  12. LQR Problem for the Augmented auxiliary System
  13. The Relation between Problem \ref{['StateLQR']} and Problem \ref{['OPFBLQR']}
  14. The VI Method for Problem \ref{['OPFBLQR']}
  15. Numerical Examples
  16. ...and 3 more sections

Figures (4)

  • Figure 1: Comparison of $P_{k}^{{\rho}}$, $K_{k}^{{\rho}}$ with the desired values ${P}_\rho^{*}$, ${K}_\rho^{*}$
  • Figure 2: Plots of the system output $y$ and the reference signals $-Fv$ after control policy updated.
  • Figure 3: Comparison of $P_{k}^{{\rho}}$, $K_{k}^{{\rho}}$ with the desired values ${P}_\rho^{*}$, ${K}_\rho^{*}$
  • Figure 4: Plots of the system output $y$ and the reference signals $-Fv$ after control policy updated.