Robustness analysis of Adaptive Model Predictive Control for uncertain non-linear dynamic systems using s-gap metric...

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.