# A neural network-based approach to hybrid systems identification for control

arXiv: https://arxiv.org/abs/2404.01814 · HTML: https://mlsanity.com/paper/2404.01814/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 67 references that are in the map.
- First posted on arXiv 2 Apr 2024.

## Builds on (most cited first, 21 of 21)

- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Learning Particle Dynamics for Manipulating Rigid Bodies, Deformable Objects, and Fluids](https://mlsanity.com/paper/1810.01566/) (2018)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [Nonlinear System Identification: A User-Oriented Roadmap](https://mlsanity.com/paper/1902.00683/) (2019)
- [Continuous-time system identification with neural networks: Model structures and fitting criteria](https://mlsanity.com/paper/2006.02915/) (2020)
- [Deep Convolutional Networks in System Identification](https://mlsanity.com/paper/1909.01730/) (2019)
- [Model structures and fitting criteria for system identification with neural networks](https://mlsanity.com/paper/1911.13034/) (2019)
- [Reliably-stabilizing piecewise-affine neural network controllers](https://mlsanity.com/paper/2111.07183/) (2021)
- [On the adaptation of recurrent neural networks for system identification](https://mlsanity.com/paper/2201.08660/) (2022)
- [Modeling Design and Control Problems Involving Neural Network Surrogates](https://mlsanity.com/paper/2111.10489/) (2021)
- [Learning Queuing Networks by Recurrent Neural Networks](https://mlsanity.com/paper/2002.10788/) (2020)
- [Learning Linear Complementarity Systems](https://mlsanity.com/paper/2112.13284/) (2021)
- [Strong Stationarity Conditions for Optimal Control of Hybrid Systems](https://mlsanity.com/paper/1507.02878/) (2015)
- [On the complexity of piecewise affine system identification](https://mlsanity.com/paper/1509.02348/) (2015)
- [System Identification for Hybrid Systems using Neural Networks](https://mlsanity.com/paper/1911.12663/) (2019)
- [Computationally efficient predictive control based on ANN state-space models](https://mlsanity.com/paper/2303.17305/) (2023)
- [Shrinkage Strategies for Structure Selection and Identification of Piecewise Affine Models](https://mlsanity.com/paper/2010.01520/) (2020)
- [A Sequential Convex Programming Approach to Solving Quadratic Programs and Optimal Control Problems with Linear Complementarity Constraints](https://mlsanity.com/paper/2103.05965/) (2021)
- [Robust stabilization of polytopic systems via fast and reliable neural network-based approximations](https://mlsanity.com/paper/2204.13209/) (2022)
- [Solving mathematical programs with complementarity constraints arising in nonsmooth optimal control](https://mlsanity.com/paper/2312.11022/) (2023)

## Abstract (arXiv)

We consider the problem of designing a machine learning-based model of an unknown dynamical system from a finite number of (state-input)-successor state data points, such that the model obtained is also suitable for optimal control design. We adopt a neural network (NN) architecture that, once suitably trained, yields a hybrid system with continuous piecewise-affine (PWA) dynamics that is differentiable with respect to the network's parameters, thereby enabling the use of derivative-based training procedures. We show that a careful choice of our NN's weights produces a hybrid system model with structural properties that are highly favorable when used as part of a finite horizon optimal control problem (OCP). Specifically, we rely on available results to establish that optimal solutions with strong local optimality guarantees can be computed via nonlinear programming (NLP), in contrast to classical OCPs for general hybrid systems which typically require mixed-integer optimization. Besides being well-suited for optimal control design, numerical simulations illustrate that our NN-based technique enjoys very similar performance to state-of-the-art system identification methods for hybrid systems and it is competitive on nonlinear benchmarks.