Observer-Side Parameter Estimation For Adaptive Control

TL;DR

This paper investigates observer-side parameter estimation in adaptive control, aiming to unify state and parameter estimation within the observer framework and proposing a new robust technique inspired by concurrent learning.

Contribution

It provides a detailed comparison of observer-side parameter estimation with traditional adaptive control and introduces a novel method to enhance robustness.

Findings

Enhanced robustness of observer-based adaptive control.

Improved stability proofs for combined observer and adaptive update.

Demonstrated potential for better integration of probabilistic information.

Abstract

In adaptive control, a controller is precisely designed for a certain model of the system, but that model's parameters are updated online by another mechanism called the adaptive update. This allows the controller to aim for the benefits of exact model knowledge while simultaneously remaining robust to model uncertainty. Like most nonlinear controllers, adaptive controllers are often designed and analyzed under the assumption of deterministic full state feedback. However, doing so inherently decouples the adaptive update mechanism from the probabilistic information provided by modern state observers. The simplest way to reconcile this is to let the observer produce both state estimates and model parameter estimates, so that all probabilistic information is shared within the framework of the observer. While this technique is becoming increasingly common, it is still not widely accepted due to a lack of general closed-loop stability proofs. In this thesis, we will investigate observer-side parameter estimation for adaptive control by precisely juxtaposing its mechanics against the current, widely accepted adaptive control designs. Additionally, we will propose a new technique that increases the robustness of observer-based adaptive control by following the same line of reasoning used for the popular concurrent learning method.