# Infinite-Horizon Value Function Approximation for Model Predictive Control

arXiv: https://arxiv.org/abs/2502.06760 · HTML: https://mlsanity.com/paper/2502.06760/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Feb 2025.

## Built on by (most cited first, 4 of 4)

- [Value-guided action planning with JEPA world models](https://mlsanity.com/paper/2601.00844/) (2025)
- [Generative Models From and For Sampling-Based MPC: A Bootstrapped Approach For Adaptive Contact-Rich Manipulation](https://mlsanity.com/paper/2510.14643/) (2025)
- [CACTO-BIC: Scalable Actor-Critic Learning via Biased Sampling and GPU-Accelerated Trajectory Optimization](https://mlsanity.com/paper/2602.19699/) (2026)
- [Warm-Starting Collision-Free Model Predictive Control With Object-Centric Diffusion](https://mlsanity.com/paper/2601.02873/) (2026)

## Abstract (arXiv)

Model Predictive Control has emerged as a popular tool for robots to generate complex motions. However, the real-time requirement has limited the use of hard constraints and large preview horizons, which are necessary to ensure safety and stability. In practice, practitioners have to carefully design cost functions that can imitate an infinite horizon formulation, which is tedious and often results in local minima. In this work, we study how to approximate the infinite horizon value function of constrained optimal control problems with neural networks using value iteration and trajectory optimization. Furthermore, we experimentally demonstrate how using this value function approximation as a terminal cost provides global stability to the model predictive controller. The approach is validated on two toy problems and a real-world scenario with online obstacle avoidance on an industrial manipulator where the value function is conditioned to the goal and obstacle.