# Assured Neural Network Architectures for Control and Identification of Nonlinear Systems

arXiv: https://arxiv.org/abs/2109.10298 · HTML: https://mlsanity.com/paper/2109.10298/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 43 references that are in the map.
- First posted on arXiv 21 Sep 2021.

## Builds on (most cited first, 14 of 14)

- [Neural Architecture Search with Reinforcement Learning](https://mlsanity.com/paper/1611.01578/) (2016)
- [Learning Transferable Architectures for Scalable Image Recognition](https://mlsanity.com/paper/1707.07012/) (2017)
- [End to End Learning for Self-Driving Cars](https://mlsanity.com/paper/1604.07316/) (2016)
- [Regularized Evolution for Image Classifier Architecture Search](https://mlsanity.com/paper/1802.01548/) (2018)
- [SNAS: Stochastic Neural Architecture Search](https://mlsanity.com/paper/1812.09926/) (2018)
- [Designing Neural Network Architectures using Reinforcement Learning](https://mlsanity.com/paper/1611.02167/) (2016)
- [Efficient Multi-objective Neural Architecture Search via Lamarckian Evolution](https://mlsanity.com/paper/1804.09081/) (2018)
- [Optimal Control Via Neural Networks: A Convex Approach](https://mlsanity.com/paper/1805.11835/) (2018)
- [Nonlinear Systems Identification Using Deep Dynamic Neural Networks](https://mlsanity.com/paper/1610.01439/) (2016)
- [AReN: Assured ReLU NN Architecture for Model Predictive Control of LTI Systems](https://mlsanity.com/paper/1911.01608/) (2019)
- [Two-Level Lattice Neural Network Architectures for Control of Nonlinear Systems](https://mlsanity.com/paper/2004.09628/) (2020)
- [System Identification for Hybrid Systems using Neural Networks](https://mlsanity.com/paper/1911.12663/) (2019)
- [Robust Approximate Simulation for Hierarchical Control of Linear Systems under Disturbances](https://mlsanity.com/paper/2003.04136/) (2020)
- [Stability Analysis of Complementarity Systems with Neural Network Controllers](https://mlsanity.com/paper/2011.07626/) (2020)

## 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 assurance that it is sufficiently parametrized to control a nonlinear system; i.e. control the system to satisfy a given formal specification. This is unlike current techniques, which provide no assurances on the resultant architecture. Moreover, our approach requires only limited knowledge of the underlying nonlinear system and specification. We assume only that the specification can be satisfied by a Lipschitz-continuous controller with a known bound on its Lipschitz constant; the specific controller need not be known. From this assumption, we bound the number of affine functions needed to construct a Continuous Piecewise Affine (CPWA) function that can approximate any Lipschitz-continuous controller that satisfies the specification. Then we connect this CPWA to a NN architecture using the authors' recent results on the Two-Level Lattice (TLL) NN architecture; the TLL architecture was shown to be parameterized by the number of affine functions present in the CPWA function it realizes.