# An Online Learning Approach to Model Predictive Control

## TL;DR

This paper introduces DMD-MPC, a novel online learning-based framework for model predictive control that unifies and extends existing MPC techniques, demonstrated through simulations and real-world experiments.

## Contribution

It presents DMD-MPC, a new algorithm linking MPC with online learning, enabling principled design and extension of MPC methods.

## Key findings

- DMD-MPC generalizes many existing MPC algorithms.
- The approach is effective in simulated cartpole and real-world driving tasks.
- Videos demonstrate practical applicability of the proposed methods.

## Abstract

Model predictive control (MPC) is a powerful technique for solving dynamic control tasks. In this paper, we show that there exists a close connection between MPC and online learning, an abstract theoretical framework for analyzing online decision making in the optimization literature. This new perspective provides a foundation for leveraging powerful online learning algorithms to design MPC algorithms. Specifically, we propose a new algorithm based on dynamic mirror descent (DMD), an online learning algorithm that is designed for non-stationary setups. Our algorithm, Dynamic Mirror Descent Model Predictive Control (DMD-MPC), represents a general family of MPC algorithms that includes many existing techniques as special instances. DMD-MPC also provides a fresh perspective on previous heuristics used in MPC and suggests a principled way to design new MPC algorithms. In the experimental section of this paper, we demonstrate the flexibility of DMD-MPC, presenting a set of new MPC algorithms on a simple simulated cartpole and a simulated and real-world aggressive driving task. Videos of the real-world experiments can be found at https://youtu.be/vZST3v0_S9w and https://youtu.be/MhuqiHo2t98.