# Flexible-step Model Predictive Control based on Generalized Lyapunov Functions

arXiv: https://arxiv.org/abs/2211.02780 · HTML: https://mlsanity.com/paper/2211.02780/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Nov 2022.

## Built on by (most cited first, 1 of 1)

- [Certifying Stability of Reinforcement Learning Policies using Generalized Lyapunov Functions](https://mlsanity.com/paper/2505.10947/) (2025)

## Abstract (arXiv)

We present a novel nonlinear model predictive control (MPC) scheme with relaxed stability criteria, based on the idea of generalized discrete-time control Lyapunov functions. These functions need to satisfy an average descent over a finite window of time, rather than a descent at every time step. One feature of this scheme is that it allows for implementing a flexible number of control inputs in each iteration, in a computationally attractive manner, while guaranteeing recursive feasibility and stability. The benefits of our flexible-step implementation are also demonstrated in an application to nonholonomic systems, where the one-step standard implementation may suffer from lack of asymptotic convergence.