# Episodic Learning with Control Lyapunov Functions for Uncertain Robotic Systems

## TL;DR

This paper introduces a machine learning framework using Control Lyapunov Functions to adaptively handle model uncertainties in robotic systems, improving stability and performance through iterative updates.

## Contribution

It presents a novel method that combines CLFs with iterative learning to enhance control robustness under uncertainty in robotics.

## Key findings

- Significant performance improvements on a Segway simulation.
- Effective adaptation to parametric uncertainty and unmodeled dynamics.
- Development of a stabilizing quadratic program controller.

## Abstract

Many modern nonlinear control methods aim to endow systems with guaranteed properties, such as stability or safety, and have been successfully applied to the domain of robotics. However, model uncertainty remains a persistent challenge, weakening theoretical guarantees and causing implementation failures on physical systems. This paper develops a machine learning framework centered around Control Lyapunov Functions (CLFs) to adapt to parametric uncertainty and unmodeled dynamics in general robotic systems. Our proposed method proceeds by iteratively updating estimates of Lyapunov function derivatives and improving controllers, ultimately yielding a stabilizing quadratic program model-based controller. We validate our approach on a planar Segway simulation, demonstrating substantial performance improvements by iteratively refining on a base model-free controller.