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Identification For Control Based on Neural Networks: Approximately Linearizable Models

Maxime Thieffry, Alexandre Hache, Mohamed Yagoubi, Philippe Chevrel

TL;DR

A control-oriented identification scheme for efficient control design and stability analysis of nonlinear systems, using neural networks to identify a discrete-time nonlinear state-space model to approximate time-domain input-output behavior of a nonlinear system.

Abstract

This work presents a control-oriented identification scheme for efficient control design and stability analysis of nonlinear systems. Neural networks are used to identify a discrete-time nonlinear state-space model to approximate time-domain input-output behavior of a nonlinear system. The network is constructed such that the identified model is approximately linearizable by feedback, ensuring that the control law trivially follows from the learning stage. After the identification and quasi-linearization procedures, linear control theory comes at hand to design robust controllers and study stability of the closed-loop system. The effectiveness and interest of the methodology are illustrated throughout the paper on popular benchmarks for system identification.

Identification For Control Based on Neural Networks: Approximately Linearizable Models

TL;DR

A control-oriented identification scheme for efficient control design and stability analysis of nonlinear systems, using neural networks to identify a discrete-time nonlinear state-space model to approximate time-domain input-output behavior of a nonlinear system.

Abstract

This work presents a control-oriented identification scheme for efficient control design and stability analysis of nonlinear systems. Neural networks are used to identify a discrete-time nonlinear state-space model to approximate time-domain input-output behavior of a nonlinear system. The network is constructed such that the identified model is approximately linearizable by feedback, ensuring that the control law trivially follows from the learning stage. After the identification and quasi-linearization procedures, linear control theory comes at hand to design robust controllers and study stability of the closed-loop system. The effectiveness and interest of the methodology are illustrated throughout the paper on popular benchmarks for system identification.
Paper Structure (18 sections, 19 equations, 3 figures, 6 tables)

This paper contains 18 sections, 19 equations, 3 figures, 6 tables.

Table of Contents

  1. Introduction
  2. Context and Related Works
  3. Problem Statement and Contributions
  4. Notations
  5. Approximately feedback-linearizable neural state-space models
  6. Definitions
  7. Identification procedure
  8. Network structure
  9. Software Implementation
  10. Initialization
  11. Implementation of Cost Function
  12. Illustrations of training results
  13. Prey-Predator system
  14. Closed-loop analysis
  15. Approximate Linearization
  16. ...and 3 more sections

Figures (3)

  • Figure 1: Control architecture for approximate feedback-linearization.
  • Figure 2: Training results for the Wiener-Hammerstein system. Blue: real output measurements, Red: error between real output and LTI model, Yellow: error between real output and AL-SSNN model \ref{['eq:ssnn_flin']}.
  • Figure 3: Training results for the prey-predator system. Blue: output measurements, Red: error between real output and LTI model, Yellow: error between real output and AL-SSNN model \ref{['eq:ssnn_flin']}.