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Composite Learning Adaptive Control under Non-Persistent Partial Excitation

Jiajun Shen, Wei Wang, Changyun Wen, Jinhu Lu

TL;DR

This work introduces a composite learning adaptive control framework that relaxes excitation requirements by using spectral decomposition of the LRE to collect historical excitation and separate parameter estimation into excited and unexcited components. It combines composite learning with μ-modification in a Lyapunov-based update law and proves that under non-persistent partial excitation the control error and excited parameter error converge to zero while the unexcited component remains bounded; the method is extended to high-order systems via RBFNN and dynamic surface control, achieving semi-global stability. Simulations on a two-link robot arm, a first-order uncertain system, and a third-order disturbed system validate the theory and show robustness improvements.

Abstract

This paper focuses on relaxing the excitation conditions for the adaptive control of uncertain nonlinear systems. By adopting the spectral decomposition technique, a linear regression equation (LRE) is constructed to quantitatively collect historical excitation information, based on which the parameter estimation error is decomposed into the excited component and the unexcited component. By sufficiently utilizing the collected excitation information, the composite learning and μ-modification terms are designed and incorporated into the "Lyapunov-based" parameter update law. By developing a novel Lyapunov function, it is demonstrated that under non-persistent partial excitation, the control error and the excited parameter estimation error component converge to zero, while the unexcited component remains bounded. Furthermore, the proposed adaptive control scheme can effectively eliminate the effects of parametric uncertainties and enhance the robustness of the closed-loop systems. Simulation results are provided to verify the theoretical findings.

Composite Learning Adaptive Control under Non-Persistent Partial Excitation

TL;DR

This work introduces a composite learning adaptive control framework that relaxes excitation requirements by using spectral decomposition of the LRE to collect historical excitation and separate parameter estimation into excited and unexcited components. It combines composite learning with μ-modification in a Lyapunov-based update law and proves that under non-persistent partial excitation the control error and excited parameter error converge to zero while the unexcited component remains bounded; the method is extended to high-order systems via RBFNN and dynamic surface control, achieving semi-global stability. Simulations on a two-link robot arm, a first-order uncertain system, and a third-order disturbed system validate the theory and show robustness improvements.

Abstract

This paper focuses on relaxing the excitation conditions for the adaptive control of uncertain nonlinear systems. By adopting the spectral decomposition technique, a linear regression equation (LRE) is constructed to quantitatively collect historical excitation information, based on which the parameter estimation error is decomposed into the excited component and the unexcited component. By sufficiently utilizing the collected excitation information, the composite learning and μ-modification terms are designed and incorporated into the "Lyapunov-based" parameter update law. By developing a novel Lyapunov function, it is demonstrated that under non-persistent partial excitation, the control error and the excited parameter estimation error component converge to zero, while the unexcited component remains bounded. Furthermore, the proposed adaptive control scheme can effectively eliminate the effects of parametric uncertainties and enhance the robustness of the closed-loop systems. Simulation results are provided to verify the theoretical findings.
Paper Structure (14 sections, 76 equations, 11 figures, 2 tables)

This paper contains 14 sections, 76 equations, 11 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Contributions
  4. Composite Learning Adaptive Control
  5. Problem Formulation and Preliminaries
  6. Design and Analysis of Linear Regression Equation
  7. Decomposition of Parameter Estimation Error
  8. Adaptive Control Design and Stability Analysis
  9. Composite Learning Adaptive Dynamic Surface Control With RBFNN
  10. Simulation Results
  11. Simulation Results of a Two-Link Planar Robot Arm
  12. Simulation Results of a First-Order Uncertain System under Sufficient and Non-Persistent Partial Excitation
  13. Simulation Results of a Third-Order System under Unstructured Uncertainties and External Disturbances
  14. Conclusion

Figures (11)

  • Figure 1: Illustrating figure for the proposed composite learning adaptive control framework.
  • Figure 2: Illustrating figure for the forgetting factor
  • Figure 3: Illustrating figure for $\lambda^+_{\min} (W(t))$ and $t_s$.
  • Figure 4: Illustrating figure for $V_{e,\kappa}(t)$ and the convergence bounds.
  • Figure 5: Simulation results in Case A. I.
  • ...and 6 more figures

Theorems & Definitions (4)

  • proof
  • proof
  • proof
  • proof