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Synchronisation-Oriented Design Approach for Adaptive Control

Namhoon Cho, Seokwon Lee, Hyo-Sang Shin

TL;DR

It is suggested that synchronisation can be a reasonable design principle allowing a more holistic and systematic approach to the design of adaptive control systems for improved transient characteristics.

Abstract

This study presents a synchronisation-oriented perspective towards adaptive control which views model-referenced adaptation as synchronisation between actual and virtual dynamic systems. In the context of adaptation, model reference adaptive control methods make the state response of the actual plant follow a reference model. In the context of synchronisation, consensus methods involving diffusive coupling induce a collective behaviour across multiple agents. We draw from the understanding about the two time-scale nature of synchronisation motivated by the study of blended dynamics. The synchronisation-oriented approach consists in the design of a coupling input to achieve desired closed-loop error dynamics followed by the input allocation process to shape the collective behaviour. We suggest that synchronisation can be a reasonable design principle allowing a more holistic and systematic approach to the design of adaptive control systems for improved transient characteristics. Most notably, the proposed approach enables not only constructive derivation but also substantial generalisation of the previously developed closed-loop reference model adaptive control method. Practical significance of the proposed generalisation lies at the capability to improve the transient response characteristics and mitigate the unwanted peaking phenomenon at the same time.

Synchronisation-Oriented Design Approach for Adaptive Control

TL;DR

It is suggested that synchronisation can be a reasonable design principle allowing a more holistic and systematic approach to the design of adaptive control systems for improved transient characteristics.

Abstract

This study presents a synchronisation-oriented perspective towards adaptive control which views model-referenced adaptation as synchronisation between actual and virtual dynamic systems. In the context of adaptation, model reference adaptive control methods make the state response of the actual plant follow a reference model. In the context of synchronisation, consensus methods involving diffusive coupling induce a collective behaviour across multiple agents. We draw from the understanding about the two time-scale nature of synchronisation motivated by the study of blended dynamics. The synchronisation-oriented approach consists in the design of a coupling input to achieve desired closed-loop error dynamics followed by the input allocation process to shape the collective behaviour. We suggest that synchronisation can be a reasonable design principle allowing a more holistic and systematic approach to the design of adaptive control systems for improved transient characteristics. Most notably, the proposed approach enables not only constructive derivation but also substantial generalisation of the previously developed closed-loop reference model adaptive control method. Practical significance of the proposed generalisation lies at the capability to improve the transient response characteristics and mitigate the unwanted peaking phenomenon at the same time.
Paper Structure (32 sections, 1 theorem, 43 equations, 8 figures, 1 table)

This paper contains 32 sections, 1 theorem, 43 equations, 8 figures, 1 table.

Table of Contents

  1. Introduction
  2. Synchronisation-Oriented Approach to Adaptive Control
  3. System Description
  4. Adaptive Control as Two-Agent Synchronisation
  5. Two Time-Scale Nature of Adaptive Control
  6. Coupling Input Allocation
  7. Design Considerations
  8. Desired Synchronisation Dynamics
  9. Best Possible Blended Dynamics
  10. Uncertainty Approximation
  11. Relation to Existing Model Reference Adaptive Control Methods
  12. Direct MRAC with Open-Loop Reference Model
  13. Direct MRAC with Closed-Loop Reference Model
  14. New MRAC Methods Based on Proposed Framework
  15. Numerical Simulation
  16. ...and 17 more sections

Key Result

Theorem 1

Consider the closed-loop system consisting of $\Sigma_{e}^{CL}$ given by Eq. Eq:sys_e_CL and the adaptation law given by Eq. Eq:theta_hat_dot where the uncertainty is modelled as in Eq. Eq:Delta_linear. Suppose that then $\mathbf{e}_{I}^{l}\left(t\right) \rightarrow 0$ as $t\rightarrow \infty$. Furthermore, provided in addition to the above conditions that then $\left(\mathbf{e}_{I}^{l}\left(t\r

Figures (8)

  • Figure 1: Angle-of-Attack $\alpha$
  • Figure 2: Pitch Rate $q$
  • Figure 3: Elevator Deflection $\delta_{e}$
  • Figure 4: True Uncertainty $\Delta$ and Approximated Uncertainty
  • Figure 5: Norm of Tracking Error $\left\|e\right\|$
  • ...and 3 more figures

Theorems & Definitions (11)

  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4
  • Remark A.1
  • Remark B.1
  • Theorem 1
  • proof
  • Remark B.2
  • Remark B.3
  • ...and 1 more