# Modeling and Control of Deep Sign-Definite Dynamics with Application to Hybrid Powertrain Control

arXiv: https://arxiv.org/abs/2509.19869 · HTML: https://mlsanity.com/paper/2509.19869/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 20 references that are in the map.
- First posted on arXiv 24 Sep 2025.

## Builds on (most cited first, 6 of 6)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [OSQP: An Operator Splitting Solver for Quadratic Programs](https://mlsanity.com/paper/1711.08013/) (2017)
- [Regularity Properties of Optimization-Based Controllers](https://mlsanity.com/paper/2311.13167/) (2023)
- [Learning Stable Koopman Embeddings for Identification and Control](https://mlsanity.com/paper/2401.08153/) (2024)
- [Learning Exactly Linearizable Deep Dynamics Models](https://mlsanity.com/paper/2311.18261/) (2023)

## Built on by (most cited first, 1 of 1)

- [Convex Chance-Constrained Stochastic Control under Uncertain Specifications with Application to Learning-Based Hybrid Powertrain Control](https://mlsanity.com/paper/2601.18313/) (2026)

## Abstract (arXiv)

Data-driven control increasingly relies on deep models for complex systems whose first-principles models are difficult to obtain. For reliable deployment, however, learned dynamics should respect physical structure and lead to tractable optimal control. We introduce sign constraints, namely sign restrictions on Jacobian entries, as a unified description of monotonicity, positivity, and sign-definiteness. For exactly linearizable deep dynamics, we provide structural conditions and neural-network parameterizations that enforce these constraints by construction. The same structure also allows model predictive control to be formulated as a convex quadratic program or as a convex relaxation, yielding a unique optimizer and a Lipschitz continuous control law. Applications to a three-tank system and a hybrid powertrain demonstrate that the proposed approach offers improved extrapolation performance and smoother control inputs compared with competing nonconvex formulations.