# Training Classifiers For Feedback Control

## TL;DR

This paper proposes a method for training classifiers for feedback control systems that use high-dimensional sensor data, focusing on stability and performance, demonstrated through a navigation case study.

## Contribution

It introduces a control-theoretic training approach for classifiers in feedback control, ensuring stability and performance without explicit state estimation.

## Key findings

- Effective classifier training using projected gradient descent.
- Improved stability in feedback control with learned classifiers.
- Successful application to sensor-based navigation.

## Abstract

One approach for feedback control using high dimensional and rich sensor measurements is to classify the measurement into one out of a finite set of situations, each situation corresponding to a (known) control action. This approach computes a control action without estimating the state. Such classifiers are typically learned from a finite amount of data using supervised machine learning algorithms. We model the closed-loop system resulting from control with feedback from classifier outputs as a piece-wise affine differential inclusion. We show how to train a linear classifier based on performance measures related to learning from data and the local stability properties of the resulting closed-loop system. The training method is based on the projected gradient descent algorithm. We demonstrate the advantage of training classifiers using control-theoretic properties on a case study involving navigation using range-based sensors.