Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Robust Adaptive Learning Control for a Class of Non-affine Nonlinear Systems

Shuai Gao, Dong Shen, Abdelhamid Tayebi

TL;DR

The paper tackles robust tracking for uncertain non-affine nonlinear systems with high relative degree under iteration-varying references. It develops a robust AILC framework that blends a gradient-descent parameter adaptation law with a state estimator and both implicit and explicit schemes to compute the non-affine control input via contraction mappings. Theoretical results establish convergence and bounded tracking error in the presence of disturbances, and a numerical iterative method provides a practical, implementable input with guaranteed approximation accuracy. Two simulations, including a non-affine single-input system and a double inverted pendulum, demonstrate superior tracking performance and disturbance robustness compared to existing DDILC methods. The work offers a direct, neural-free approach to non-affine ILC with provable guarantees and practical numerical implementation strategies.

Abstract

We address the tracking problem for a class of uncertain non-affine nonlinear systems with high relative degrees, performing non-repetitive tasks. We propose a rigorously proven, robust adaptive learning control scheme that relies on a gradient descent parameter adaptation law to handle the unknown time-varying parameters of the system, along with a state estimator that estimates the unmeasurable state variables. Furthermore, despite the inherently complex nature of the non-affine system, we provide an explicit iterative computation method to facilitate the implementation of the proposed control scheme. The paper includes a thorough analysis of the performance of the proposed control strategy, and simulation results are presented to demonstrate the effectiveness of the approach.

Robust Adaptive Learning Control for a Class of Non-affine Nonlinear Systems

TL;DR

The paper tackles robust tracking for uncertain non-affine nonlinear systems with high relative degree under iteration-varying references. It develops a robust AILC framework that blends a gradient-descent parameter adaptation law with a state estimator and both implicit and explicit schemes to compute the non-affine control input via contraction mappings. Theoretical results establish convergence and bounded tracking error in the presence of disturbances, and a numerical iterative method provides a practical, implementable input with guaranteed approximation accuracy. Two simulations, including a non-affine single-input system and a double inverted pendulum, demonstrate superior tracking performance and disturbance robustness compared to existing DDILC methods. The work offers a direct, neural-free approach to non-affine ILC with provable guarantees and practical numerical implementation strategies.

Abstract

We address the tracking problem for a class of uncertain non-affine nonlinear systems with high relative degrees, performing non-repetitive tasks. We propose a rigorously proven, robust adaptive learning control scheme that relies on a gradient descent parameter adaptation law to handle the unknown time-varying parameters of the system, along with a state estimator that estimates the unmeasurable state variables. Furthermore, despite the inherently complex nature of the non-affine system, we provide an explicit iterative computation method to facilitate the implementation of the proposed control scheme. The paper includes a thorough analysis of the performance of the proposed control strategy, and simulation results are presented to demonstrate the effectiveness of the approach.
Paper Structure (20 sections, 10 theorems, 87 equations, 8 figures, 1 table)

This paper contains 20 sections, 10 theorems, 87 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Tracking Feasibility and AILC Design
  4. Tracking Feasibility Analysis
  5. GDPA Scheme
  6. State Estimation
  7. Implicit AILC Design
  8. Convergence Analysis
  9. Explicit AILC Design
  10. Numerical Simulations
  11. Example 1
  12. Example 2
  13. Conclusions
  14. Proof of Proposition \ref{['pp1']}
  15. Proof of Theorem \ref{['Th1']}
  16. ...and 5 more sections

Key Result

Proposition 1

Under Assumption assu1, for any $t\in \{0,1,\cdots$, $T-\rho\}$ and $k\in \mathbb{Z}^+$, there exists a unique ideal control input $u=u_k^\ast(t)$ such that trackingequation holds. In addition, there exists a known contraction mapping $\mathcal{T}$ such that $u_k^\ast(t)$ is the fixed point of $\mat

Figures (8)

  • Figure 1: Block diagram of the AILC scheme.
  • Figure 2: Maximum and average tracking errors under AILC and DDILC in Example 1.
  • Figure 3: Tracking profiles for the iteration-varying reference trajectory under AILC and DDILC in Example 1.
  • Figure 4: Tracking error under different disturbances in Example 1.
  • Figure 5: Maximum and average tracking errors of each iteration in Example 2 without disturbance.
  • ...and 3 more figures

Theorems & Definitions (17)

  • Remark 1
  • Remark 2
  • Proposition 1
  • Proposition 2
  • Remark 3
  • Theorem 1
  • Corollary 1
  • Corollary 2
  • Lemma 1
  • Remark 4
  • ...and 7 more