# Model Predictive Control, Cost Controllability, and Homogeneity *

## TL;DR

This paper develops a new MPC design approach using homogeneous approximations to ensure asymptotic stability even when linearization fails, by establishing cost controllability without terminal costs or constraints.

## Contribution

It introduces a novel MPC scheme based on homogeneous approximations and proves stability through cost controllability, bypassing the need for terminal costs or constraints.

## Key findings

- MPC with homogeneous cost design guarantees stability.
- Cost controllability is verified for this class of systems.
- Stability is achieved without terminal costs or constraints.

## Abstract

We are concerned with the design of Model Predictive Control (MPC) schemes such that asymptotic stability of the resulting closed loop is guaranteed even if the linearization at the desired set point fails to be stabilizable. Therefore, we propose to construct the stage cost based on the homogeneous approximation and rigorously show that applying MPC yields an asymp-totically stable closed-loop behavior if the homogeneous approximation is asymptotically null controllable. To this end, we verify cost controllability-a condition relating the current state, the stage cost, and the growth of the value function w.r.t. time-for this class of systems in order to provide stability and performance guarantees for the proposed MPC scheme without stabilizing terminal costs or constraints.