Event-triggered Learning for Linear Quadratic Control

TL;DR

This paper introduces an event-triggered learning framework for linear quadratic control that detects model inaccuracies using probabilistic bounds and triggers model updates only when necessary, improving control performance.

Contribution

It proposes a novel probabilistic trigger mechanism based on Chernoff bounds for when to update models in linear quadratic control, enhancing efficiency and robustness.

Findings

The bounds are shown to be tight through experiments.

The algorithm effectively distinguishes model mismatch from noise.

Numerical and hardware tests validate the approach.

Abstract

When models are inaccurate, the performance of model-based control will degrade. For linear quadratic control, an event-triggered learning framework is proposed that automatically detects inaccurate models and triggers the learning of a new process model when needed. This is achieved by analyzing the probability distribution of the linear quadratic cost and designing a learning trigger that leverages Chernoff bounds. In particular, whenever empirically observed cost signals are located outside the derived confidence intervals, we can provably guarantee that this is with high probability due to a model mismatch. With the aid of numerical and hardware experiments, we demonstrate that the proposed bounds are tight and that the event-triggered learning algorithm effectively distinguishes between inaccurate models and probabilistic effects such as process noise. Thus, a structured approach is obtained that decides when model learning is beneficial.