# Model predictive control with stage cost shaping inspired by reinforcement learning

## TL;DR

This paper investigates a model predictive control method that incorporates reinforcement learning principles to shape the stage cost, aiming to analyze its suboptimality and compare its performance to the infinite-horizon optimal control.

## Contribution

It introduces a novel stage cost shaping approach inspired by reinforcement learning within the MPC framework and provides a suboptimality analysis relating it to the infinite-horizon value function.

## Key findings

- Suboptimality bounds derived for the proposed MPC variant.
- Case studies demonstrate effectiveness across various initial conditions.
- Stage cost shaping improves control performance in tested systems.

## Abstract

This work presents a suboptimality study of a particular model predictive control with a stage cost shaping based on the ideas of reinforcement learning. The focus of the suboptimality study is to derive quantities relating the infinite-horizon cost function under the said variant of model predictive control to the respective infinite-horizon value function. The basis control scheme involves usual stabilizing constraints comprising of a terminal set and a terminal cost in the form of a local Lyapunov function. The stage cost is adapted using the principles of Q-learning, a particular approach to reinforcement learning. The work is concluded by case studies with two systems for wide ranges of initial conditions.