# Online learning with stability guarantees: A memory-based real-time model predictive controller

## TL;DR

This paper introduces a data-driven real-time MPC scheme that learns the value function online, ensuring stability and improving control performance by utilizing historical data for better warm starts.

## Contribution

It presents a novel online learning method for MPC that guarantees stability and convergence, enhancing real-time control with data storage and learning.

## Key findings

- Warm starts become asymptotically exact
- Suboptimality diminishes over time
- Performance improves with data storage and learning

## Abstract

We propose and analyze a real-time model predictive control (MPC) scheme that utilizes stored data to improve its performance by learning the value function online with stability guarantees. For linear and nonlinear systems, a learning method is presented that makes use of basic analytic properties of the cost function and is proven to learn the MPC control law and the value function on the limit set of the closed-loop state trajectory. The main idea is to generate a smart warm start based on historical data that improves future data points and thus future warm starts. We show that these warm starts are asymptotically exact and converge to the solution of the MPC optimization problem. Thereby, the suboptimality of the applied control input resulting from the real-time requirements vanishes over time. Simulative examples show that existing real-time MPC schemes can be improved by storing data and the proposed learning scheme.