Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Discrete-time Contraction-based Control of Nonlinear Systems with Parametric Uncertainties using Neural Networks

Lai Wei, Ryan McCloy, Jie Bao

TL;DR

A contraction theory-based control approach using neural networks is developed for nonlinear chemical processes to achieve time-varying reference tracking and ensures the process stability during online simultaneous learning and control.

Abstract

In response to the continuously changing feedstock supply and market demand for products with different specifications, the processes need to be operated at time-varying operating conditions and targets (e.g., setpoints) to improve the process economy, in contrast to traditional process operations around predetermined equilibriums. In this paper, a contraction theory-based control approach using neural networks is developed for nonlinear chemical processes to achieve time-varying reference tracking. This approach leverages the universal approximation characteristics of neural networks with discrete-time contraction analysis and control. It involves training a neural network to learn a contraction metric and differential feedback gain, that is embedded in a contraction-based controller. A second, separate neural network is also incorporated into the control-loop to perform online learning of uncertain system model parameters. The resulting control scheme is capable of achieving efficient offset-free tracking of time-varying references, with a full range of model uncertainty, without the need for controller structure redesign as the reference changes. This is a robust approach that can deal with bounded parametric uncertainties in the process model, which are commonly encountered in industrial (chemical) processes. This approach also ensures the process stability during online simultaneous learning and control. Simulation examples are provided to illustrate the above approach.

Discrete-time Contraction-based Control of Nonlinear Systems with Parametric Uncertainties using Neural Networks

TL;DR

A contraction theory-based control approach using neural networks is developed for nonlinear chemical processes to achieve time-varying reference tracking and ensures the process stability during online simultaneous learning and control.

Abstract

In response to the continuously changing feedstock supply and market demand for products with different specifications, the processes need to be operated at time-varying operating conditions and targets (e.g., setpoints) to improve the process economy, in contrast to traditional process operations around predetermined equilibriums. In this paper, a contraction theory-based control approach using neural networks is developed for nonlinear chemical processes to achieve time-varying reference tracking. This approach leverages the universal approximation characteristics of neural networks with discrete-time contraction analysis and control. It involves training a neural network to learn a contraction metric and differential feedback gain, that is embedded in a contraction-based controller. A second, separate neural network is also incorporated into the control-loop to perform online learning of uncertain system model parameters. The resulting control scheme is capable of achieving efficient offset-free tracking of time-varying references, with a full range of model uncertainty, without the need for controller structure redesign as the reference changes. This is a robust approach that can deal with bounded parametric uncertainties in the process model, which are commonly encountered in industrial (chemical) processes. This approach also ensures the process stability during online simultaneous learning and control. Simulation examples are provided to illustrate the above approach.

Paper Structure

This paper contains 16 sections, 6 theorems, 29 equations, 8 figures, 3 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation and Approach
  3. Contraction Theory Overview
  4. System Description
  5. Objective and Approach
  6. Neural Network Approach to Contraction Analysis and Control of Uncertain Nonlinear Systems
  7. Model-based Data Generation
  8. DCCM Synthesis from Data
  9. Loss Function Design
  10. DCCM Neural Network Training
  11. Neural Network Embedded Contraction-based Controller
  12. Online Parameter Learning
  13. Synthesis and Implementation Summary
  14. Design Analysis
  15. Illustrative Example
  16. ...and 1 more sections

Key Result

Lemma 1

For the DCCM-based controller equ:control integral that ensures a system without uncertainty equ:pre cer sys is contracting, when parametric uncertainty is present equ:deviation control affine, the state trajectory, $x$, is driven by equ:control integral to the bounding ball around the target refere

Figures (8)

  • Figure 1: System trajectories along the state manifold $\mathcal{X}$.
  • Figure 2: Illustration of the DCCM neural network structure.
  • Figure 3: DCCM neural network training process block diagram.
  • Figure 4: Illustration of the online parameter estimation neural network training process.
  • Figure 5: Proposed neural network embedded contraction-based control scheme.
  • ...and 3 more figures

Theorems & Definitions (20)

  • Definition 1
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark 5
  • Lemma 1
  • proof
  • Remark 6
  • Remark 7
  • ...and 10 more