Adaptive Certainty-Equivalence Control With Regulation-Triggered Finite-Time Least-Squares Identification, Part II: Analysis

TL;DR

This paper provides a stability analysis for a novel regulation-triggered adaptive control method with finite-time parameter identification, addressing the challenges of hybrid system analysis and offering a practical observability check.

Contribution

It introduces a new stability proof for a regulation-triggered adaptive control approach and proposes an algorithm for verifying parameter observability in nonlinear systems.

Findings

Stability analysis for hybrid adaptive control system.

Algorithm for parameter-observability verification.

Applicability to nonlinear systems with single unknown parameter per equation.

Abstract

We present the stability analysis for the new regulation-triggered approach to adaptive control introduced in a companion paper. Due to the fact that the closed-loop system is hybrid, our proofs have essential differences from the conventional adaptive control proofs, where the Lyapunov analysis either encompasses the complete closed-loop state or is done in multiple steps through comparison or Gronwall-Bellman lemmas. In addition, we present a convenient algorithm for checking our parameter-observability assumption, which involves repeated Lie derivatives of appropriate vector fields and can be applied to the class of nonlinear control systems for which at most one unknown parameter appears in each differential equation.