# Infinite-Horizon Differentiable Model Predictive Control

arXiv: https://arxiv.org/abs/2001.02244 · HTML: https://mlsanity.com/paper/2001.02244/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Placed in Imitation learning methods, one of 13 directions in Offline RL and imitation learning from data.
- First posted on arXiv 7 Jan 2020.

## Placed in

- Offline RL and imitation learning from data / [Imitation learning methods](https://mlsanity.com/offlinerl/imitation-learning-methods/)

## Built on by (most cited first, 17 of 17)

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- [Deep Learning Explicit Differentiable Predictive Control Laws for Buildings](https://mlsanity.com/paper/2107.11843/) (2021)
- [Towards Modeling and Influencing the Dynamics of Human Learning](https://mlsanity.com/paper/2301.00901/) (2023)
- [Neural Lyapunov Differentiable Predictive Control](https://mlsanity.com/paper/2205.10728/) (2022)
- [Differentiable Predictive Control with Safety Guarantees: A Control Barrier Function Approach](https://mlsanity.com/paper/2208.02319/) (2022)
- [Learning Stochastic Parametric Differentiable Predictive Control Policies](https://mlsanity.com/paper/2203.01447/) (2022)
- [Critic as Lyapunov function (CALF): a model-free, stability-ensuring agent](https://mlsanity.com/paper/2409.09869/) (2024)
- [Learning Multiple Initial Solutions to Optimization Problems](https://mlsanity.com/paper/2411.02158/) (2024)
- [Neural Weighted A*: Learning Graph Costs and Heuristics with Differentiable Anytime A*](https://mlsanity.com/paper/2105.01480/) (2021)
- [Imitation Learning of Stabilizing Policies for Nonlinear Systems](https://mlsanity.com/paper/2109.10854/) (2021)
- [Decision-Focused Forecasting: A Differentiable Multistage Optimisation Architecture](https://mlsanity.com/paper/2405.14719/) (2024)
- [Differentiable Predictive Control for Large-Scale Urban Road Networks](https://mlsanity.com/paper/2406.10433/) (2024)
- [A novel agent with formal goal-reaching guarantees: an experimental study with a mobile robot](https://mlsanity.com/paper/2409.14867/) (2024)
- [Guiding Reinforcement Learning with Incomplete System Dynamics](https://mlsanity.com/paper/2410.16821/) (2024)
- [Model-free Reinforcement Learning for Model-based Control: Towards Safe, Interpretable and Sample-efficient Agents](https://mlsanity.com/paper/2507.13491/) (2025)

## Abstract (arXiv)

This paper proposes a differentiable linear quadratic Model Predictive Control (MPC) framework for safe imitation learning. The infinite-horizon cost is enforced using a terminal cost function obtained from the discrete-time algebraic Riccati equation (DARE), so that the learned controller can be proven to be stabilizing in closed-loop. A central contribution is the derivation of the analytical derivative of the solution of the DARE, thereby allowing the use of differentiation-based learning methods. A further contribution is the structure of the MPC optimization problem: an augmented Lagrangian method ensures that the MPC optimization is feasible throughout training whilst enforcing hard constraints on state and input, and a pre-stabilizing controller ensures that the MPC solution and derivatives are accurate at each iteration. The learning capabilities of the framework are demonstrated in a set of numerical studies.