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Data-Driven Control of Continuous-Time LTI Systems via Non-Minimal Realizations

Alessandro Bosso, Marco Borghesi, Andrea Iannelli, Giuseppe Notarstefano, Andrew R. Teel

Abstract

This article proposes an approach to design output-feedback controllers for unknown continuous-time linear time-invariant systems using only input-output data from a single experiment. To address the lack of state and derivative measurements, we introduce non-minimal realizations whose states can be observed by filtering the available data. We first apply this concept to the disturbance-free case, formulating linear matrix inequalities (LMIs) from batches of sampled signals to design a dynamic, filter-based stabilizing controller. The framework is then extended to the problem of asymptotic tracking and disturbance rejection - in short, output regulation - by incorporating an internal model based on prior knowledge of the disturbance/reference frequencies. Finally, we discuss tuning strategies for a class of multi-input multi-output systems and illustrate the method via numerical examples.

Data-Driven Control of Continuous-Time LTI Systems via Non-Minimal Realizations

Abstract

This article proposes an approach to design output-feedback controllers for unknown continuous-time linear time-invariant systems using only input-output data from a single experiment. To address the lack of state and derivative measurements, we introduce non-minimal realizations whose states can be observed by filtering the available data. We first apply this concept to the disturbance-free case, formulating linear matrix inequalities (LMIs) from batches of sampled signals to design a dynamic, filter-based stabilizing controller. The framework is then extended to the problem of asymptotic tracking and disturbance rejection - in short, output regulation - by incorporating an internal model based on prior knowledge of the disturbance/reference frequencies. Finally, we discuss tuning strategies for a class of multi-input multi-output systems and illustrate the method via numerical examples.

Paper Structure

This paper contains 28 sections, 16 theorems, 114 equations, 4 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Data-Driven Stabilization
  4. Data-Driven Output Regulation
  5. Canonical Non-Minimal Realizations
  6. Data-Driven Stabilization
  7. Data-Driven Output Regulation
  8. Design of Canonical Non-Minimal Realizations
  9. State-Feedback Scenario (C = In)
  10. SISO Output-Feedback Scenario (m = p = 1)
  11. MIMO Output-Feedback Scenario
  12. Observability Index Estimation
  13. Numerical Examples
  14. Unstable Batch Reactor Control
  15. Motion Control of a Surface Vessel
  16. ...and 13 more sections

Key Result

Lemma 1

Let Assumption hyp:ctrb_obs hold. Suppose that, given the plant matrices $A$, $B$, $C$, and the design matrices $F$, $G$, $L$, there exist matrices $\Pi \in {\mathbb{R}}^{n \times \mu}$ and $H \in {\mathbb{R}}^{p \times \mu}$ such that Then, $\Pi$ has full-row rank and the controllable and observable subsystem of eq:non-minimal_plant obeys dynamics eq:plant, with state $x = \Pi \zeta$.

Figures (4)

  • Figure 1: Implementation of the controller \ref{['eq:controller']} designed in Algorithm \ref{['alg:stabilization']}.
  • Figure 2: Implementation of the controller \ref{['eq:controller_out_reg']} designed in Algorithm \ref{['alg:out_reg']}.
  • Figure 3: Simulation run for the batch reactor (control with integral action).
  • Figure 4: Simulation run for the surface vessel example.

Theorems & Definitions (30)

  • Lemma 1
  • proof
  • Remark 1
  • Lemma 2
  • proof
  • Definition 1
  • Corollary 1
  • proof
  • Lemma 3
  • Remark 2
  • ...and 20 more