# Two-Level Lattice Neural Network Architectures for Control of Nonlinear Systems

arXiv: https://arxiv.org/abs/2004.09628 · HTML: https://mlsanity.com/paper/2004.09628/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Apr 2020.

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

- [Fast BATLLNN: Fast Box Analysis of Two-Level Lattice Neural Networks](https://mlsanity.com/paper/2111.09293/) (2021)
- [Provably Correct Training of Neural Network Controllers Using Reachability Analysis](https://mlsanity.com/paper/2102.10806/) (2021)
- [Reinforcement Learning with Formal Performance Metrics for Quadcopter Attitude Control under Non-nominal Contexts](https://mlsanity.com/paper/2107.12942/) (2021)
- [Assured Neural Network Architectures for Control and Identification of Nonlinear Systems](https://mlsanity.com/paper/2109.10298/) (2021)

## Abstract (arXiv)

In this paper, we consider the problem of automatically designing a Rectified Linear Unit (ReLU) Neural Network (NN) architecture (number of layers and number of neurons per layer) with the guarantee that it is sufficiently parametrized to control a nonlinear system. Whereas current state-of-the-art techniques are based on hand-picked architectures or heuristic based search to find such NN architectures, our approach exploits the given model of the system to design an architecture; as a result, we provide a guarantee that the resulting NN architecture is sufficient to implement a controller that satisfies an achievable specification. Our approach exploits two basic ideas. First, assuming that the system can be controlled by an unknown Lipschitz-continuous state-feedback controller with some Lipschitz constant upper-bounded by Kcont, we bound the number of affine functions needed to construct a Continuous Piecewise Affine (CPWA) function that can approximate the unknown Lipschitz-continuous controller. Second, we utilize the authors' recent results on a novel NN architecture named as the Two-Level Lattice (TLL) NN architecture, which was shown to be capable of implementing any CPWA function just from the knowledge of the number of affine functions that compromises this CPWA function.