Adaptive Control By Regulation-Triggered Batch Least-Squares Estimation of Non-Observable Parameters

TL;DR

This paper introduces a novel event-triggered adaptive control scheme using Batch Least-Squares Identification to handle non-observable parameters, ensuring global regulation and exponential convergence.

Contribution

It extends existing adaptive control methods by incorporating a Batch Least-Squares Identifier activated at event times for non-observable parameters.

Findings

Guarantees finite-time asymptotic parameter constancy.

Ensures global asymptotic regulation with exponential convergence.

Demonstrates effectiveness on wing-rock model with comparative analysis.

Abstract

The paper extends a recently proposed indirect, certainty-equivalence, event-triggered adaptive control scheme to the case of non-observable parameters. The extension is achieved by using a novel Batch Least-Squares Identifier (BaLSI), which is activated at the times of the events. The BaLSI guarantees the finite-time asymptotic constancy of the parameter estimates and the fact that the trajectories of the closed-loop system follow the trajectories of the nominal closed-loop system ("nominal" in the sense of the asymptotic parameter estimate, not in the sense of the true unknown parameter). Thus, if the nominal feedback guarantees global asymptotic stability and local exponential stability, then unlike conventional adaptive control, the newly proposed event-triggered adaptive scheme guarantees global asymptotic regulation with a uniform exponential convergence rate. The developed adaptive scheme is tested to a well-known control problem: the state regulation of the wing-rock model. Comparisons with other adaptive schemes are provided for this particular problem.