# A Guaranteed-Stable Neural Network Approach for Optimal Control of Nonlinear Systems

arXiv: https://arxiv.org/abs/2501.17333 · HTML: https://mlsanity.com/paper/2501.17333/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 39 references that are in the map.
- First posted on arXiv 28 Jan 2025.

## Builds on (most cited first, 10 of 10)

- [Lyapunov-stable neural-network control](https://mlsanity.com/paper/2109.14152/) (2021)
- [GradMax: Growing Neural Networks using Gradient Information](https://mlsanity.com/paper/2201.05125/) (2022)
- [Firefly Neural Architecture Descent: a General Approach for Growing Neural Networks](https://mlsanity.com/paper/2102.08574/) (2021)
- [Enforcing robust control guarantees within neural network policies](https://mlsanity.com/paper/2011.08105/) (2020)
- [Learning Control Lyapunov Functions from Counterexamples and Demonstrations](https://mlsanity.com/paper/1804.05285/) (2018)
- [Towards Dropout Training for Convolutional Neural Networks](https://mlsanity.com/paper/1512.00242/) (2015)
- [Adaptive Robust Model Predictive Control with Matched and Unmatched Uncertainty](https://mlsanity.com/paper/2104.08261/) (2021)
- [Navigating Local Minima in Quantized Spiking Neural Networks](https://mlsanity.com/paper/2202.07221/) (2022)
- [Neural Optimization Machine: A Neural Network Approach for Optimization](https://mlsanity.com/paper/2208.03897/) (2022)
- [Closed-Loop Model Identification and MPC-based Navigation of Quadcopters: A Case Study of Parrot Bebop 2](https://mlsanity.com/paper/2404.07267/) (2024)

## Abstract (arXiv)

A promising approach to optimal control of nonlinear systems involves iteratively linearizing the system and solving an optimization problem at each time instant to determine the optimal control input. Since this approach relies on online optimization, it can be computationally expensive, and thus unrealistic for systems with limited computing resources. One potential solution to this issue is to incorporate a Neural Network (NN) into the control loop to emulate the behavior of the optimal control scheme. Ensuring stability and reference tracking in the resulting NN-based closed-loop system requires modifications to the primary optimization problem. These modifications often introduce non-convexity and nonlinearity with respect to the decision variables, which may surpass the capabilities of existing solvers and complicate the generation of the training dataset. To address this issue, this paper develops a Neural Optimization Machine (NOM) to solve the resulting optimization problems. The central concept of a NOM is to transform the optimization challenges into the problem of training a NN. Rigorous proofs demonstrate that when a NN trained on data generated by the NOM is used in the control loop, all signals remain bounded and the system states asymptotically converge to a neighborhood around the desired equilibrium point, with a tunable proximity threshold. Simulation and experimental studies are provided to illustrate the effectiveness of the proposed methodology.