# Relaxed Logarithmic Barrier Function Based Model Predictive Control of Linear Systems

arXiv: https://arxiv.org/abs/1503.03314 · HTML: https://mlsanity.com/paper/1503.03314/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 11 Mar 2015.

## Built on by (most cited first, 8 of 8)

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- [Safe Pontryagin Differentiable Programming](https://mlsanity.com/paper/2105.14937/) (2021)
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- [Lane-Keeping Control of Autonomous Vehicles Through a Soft-Constrained Iterative LQR](https://mlsanity.com/paper/2311.16900/) (2023)
- [L3Ms -- Lagrange Large Language Models](https://mlsanity.com/paper/2410.21533/) (2024)
- [Improved Sample Complexity of Imitation Learning for Barrier Model Predictive Control](https://mlsanity.com/paper/2410.00859/) (2024)
- [Effective Virtual Reality Teleoperation of an Upper-body Humanoid with Modified Task Jacobians and Relaxed Barrier Functions for Self-Collision Avoidance](https://mlsanity.com/paper/2411.07534/) (2024)
- [Re4MPC: Reactive Nonlinear MPC for Multi-model Motion Planning via Deep Reinforcement Learning](https://mlsanity.com/paper/2506.08344/) (2025)

## Abstract (arXiv)

In this paper, we investigate the use of relaxed logarithmic barrier functions in the context of linear model predictive control. We present results that allow to guarantee asymptotic stability of the corresponding closed-loop system, and discuss further properties like performance and constraint satisfaction in dependence of the underlying relaxation. The proposed stabilizing MPC schemes are not necessarily based on an explicit terminal set or state constraint and allow to characterize the stabilizing control input sequence as the minimizer of a globally defined, continuously differentiable, and strongly convex function. The results are illustrated by means of a numerical example.