An Online Learning Analysis of Minimax Adaptive Control

TL;DR

This paper analyzes the performance of minimax adaptive control in online settings with finite model uncertainty, focusing on regret growth, robustness, and adaptation over time.

Contribution

It provides an online learning framework for minimax adaptive control with finite uncertainty sets, analyzing regret and robustness properties.

Findings

Regret growth over time is characterized under different disturbances.

Robustness of the controller influences the regret rate.

The analysis links adaptive control performance to model uncertainty and disturbance effects.

Abstract

We present an online learning analysis of minimax adaptive control for the case where the uncertainty includes a finite set of linear dynamical systems. Precisely, for each system inside the uncertainty set, we define the model-based regret by comparing the state and input trajectories from the minimax adaptive controller against that of an optimal controller in hindsight that knows the true dynamics. We then define the total regret as the worst case model-based regret with respect to all models in the considered uncertainty set. We study how the total regret accumulates over time and its effect on the adaptation mechanism employed by the controller. Moreover, we investigate the effect of the disturbance on the growth of the regret over time and draw connections between robustness of the controller and the associated regret rate.