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Data-Driven Safe Output Regulation of Strict-Feedback Linear Systems with Input Delay

Zhenxu Zhao, Ji Wang, Weiyao Lan

TL;DR

This work addresses safe output regulation for linear strict-feedback systems with significant uncertainties, including unknown input delay and disturbances. It integrates a data-driven pipeline based on Koopman operator theory and Krylov DMD to identify the plant dynamics and BaLSI for delay and input gain, then couples this with Control Barrier Functions (CBFs) and backstepping to enforce safety and achieve exponential tracking. The approach provides both full-state feedback and output-feedback designs, with finite-time exact identification of key parameters and rigorous safety guarantees under uncertainty, demonstrated via a vehicle platooning example. The result advances practical safe regulation for delay-coupled systems and offers a framework adaptable to other safety-critical, data-limited control applications with unknown dynamics.

Abstract

This paper develops a data-driven safe control framework for linear systems possessing a known strict-feedback structure, but with most plant parameters, external disturbances, and input delay being unknown. By leveraging Koopman operator theory, we utilize Krylov dynamic mode decomposition (DMD) to extract the system dynamics from measured data, enabling the reconstruction of the system and disturbance matrices. Concurrently, the batch least-squares identification (BaLSI) method is employed to identify other unknown parameters in the input channel. Using control barrier functions (CBFs) and backstepping, we first develop a full-state safe controller. Based on this, we build an output-feedback controller by performing system identification using only the output data and actuation signals as well as constructing an observer to estimate the unmeasured plant states. The proposed approach achieves: 1) finite-time identification of a substantial set of unknown system quantities, and 2) exponential convergence of the output state (the state furthest from the control input) to a reference trajectory while rigorously ensuring safety constraints. The effectiveness of the proposed method is demonstrated through a safe vehicle platooning application.

Data-Driven Safe Output Regulation of Strict-Feedback Linear Systems with Input Delay

TL;DR

This work addresses safe output regulation for linear strict-feedback systems with significant uncertainties, including unknown input delay and disturbances. It integrates a data-driven pipeline based on Koopman operator theory and Krylov DMD to identify the plant dynamics and BaLSI for delay and input gain, then couples this with Control Barrier Functions (CBFs) and backstepping to enforce safety and achieve exponential tracking. The approach provides both full-state feedback and output-feedback designs, with finite-time exact identification of key parameters and rigorous safety guarantees under uncertainty, demonstrated via a vehicle platooning example. The result advances practical safe regulation for delay-coupled systems and offers a framework adaptable to other safety-critical, data-limited control applications with unknown dynamics.

Abstract

This paper develops a data-driven safe control framework for linear systems possessing a known strict-feedback structure, but with most plant parameters, external disturbances, and input delay being unknown. By leveraging Koopman operator theory, we utilize Krylov dynamic mode decomposition (DMD) to extract the system dynamics from measured data, enabling the reconstruction of the system and disturbance matrices. Concurrently, the batch least-squares identification (BaLSI) method is employed to identify other unknown parameters in the input channel. Using control barrier functions (CBFs) and backstepping, we first develop a full-state safe controller. Based on this, we build an output-feedback controller by performing system identification using only the output data and actuation signals as well as constructing an observer to estimate the unmeasured plant states. The proposed approach achieves: 1) finite-time identification of a substantial set of unknown system quantities, and 2) exponential convergence of the output state (the state furthest from the control input) to a reference trajectory while rigorously ensuring safety constraints. The effectiveness of the proposed method is demonstrated through a safe vehicle platooning application.
Paper Structure (44 sections, 15 theorems, 105 equations, 9 figures, 1 table)

This paper contains 44 sections, 15 theorems, 105 equations, 9 figures, 1 table.

Table of Contents

  1. Introduction
  2. Output Regulation
  3. Safety-Critical Control in Complex Environments
  4. Data driven with DMD and Koopman operator
  5. Main contributions
  6. Organization
  7. Notation
  8. Problem Formulation
  9. Considered plant
  10. Control objective
  11. Control design with full state access
  12. Nominal safe controller design
  13. First transformation
  14. Second transformations
  15. Third Transformation and controller
  16. ...and 29 more sections

Key Result

Lemma 1

The high-relative-degree CBFs $h_i(t), i=1,\cdots,n$ are nonnegative under the selection of design parameters k, hk, i.e., $h_i(t)\ge 0, i=1,\cdots,n$, for time $t\ge D$.

Figures (9)

  • Figure 1: Diagram of the proposed data-driven safe control system.
  • Figure 2: Diagram of the proposed output-feedback data-driven safe control system.
  • Figure 3: Vehicle platooning with leader $E_0$, and the controlled $E_i,i=1,2$, where the safe s to be maintained are $s_{oi}$.
  • Figure 4: Distance between vehicles $E_1$ and $E_0$.
  • Figure 5: Speed and Control force of vehicle $E_1$.
  • ...and 4 more figures

Theorems & Definitions (33)

  • Lemma 1
  • proof
  • Lemma 2
  • proof
  • Remark 1
  • Lemma 3
  • proof
  • Lemma 4
  • proof
  • Lemma 5
  • ...and 23 more