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This study introduces a novel method for robust adaptive control systems, enhancing online model identification and stability. It addresses challenges in non-linear systems by integrating generalized stability margin (GSM) into adaptive model predictive control (AMPC).

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Gain boundsGraph topologyNon-linear gap metricRobust on-line identification and robust model predictive control

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Area of Science:

  • Control Engineering
  • Systems Theory
  • Robust Control

Background:

  • Robustness analysis of adaptive control systems, particularly for non-linear dynamic systems with un-modelled dynamics, remains a significant challenge.
  • Existing methods struggle to adequately address unstructured uncertainty and the interplay between controller operation and on-line model identification.

Purpose of the Study:

  • To develop a systematic solution for robust adaptive control by addressing limitations in current robust control theory.
  • To present a novel on-line identification method with convergence guarantees and establish a relationship between generalized stability margin (GSM) and identifier convergence.

Main Methods:

  • Introduced new concepts in robust control theory, including the s-gap metric and generalized stability margin (GSM).
  • Developed an on-line identification method with convergence proof based on the s-gap metric.
  • Integrated GSM into the Adaptive Model Predictive Control (AMPC) cost function using linear matrix inequality (LMI) representation for robustness.

Main Results:

  • Demonstrated a method for on-line identification with convergence guarantees in the sense of the s-gap metric.
  • Established a relationship between GSM and the identifier convergence area, ensuring stability of AMPC within a defined operating domain.
  • Identified a trade-off between attraction area size, convergence area size, and closed-loop system robustness.

Conclusions:

  • The proposed method offers a systematic solution for relating controller robustness and adaptivity in AMPC.
  • The integration of GSM constraints guarantees stability and defines the attraction area of the closed-loop system.
  • Simulations and experimental results validate the correctness and effectiveness of the proposed robust adaptive control approach.