# Learning-based Symbolic Abstractions for Nonlinear Control Systems

arXiv: https://arxiv.org/abs/2004.01879 · HTML: https://mlsanity.com/paper/2004.01879/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2020.

## Built on by (most cited first, 11 of 11)

- [Automatic nonlinear MPC approximation with closed-loop guarantees](https://mlsanity.com/paper/2312.10199/) (2023)
- [Safe exploration in reproducing kernel Hilbert spaces](https://mlsanity.com/paper/2503.10352/) (2025)
- [PACSBO: Probably approximately correct safe Bayesian optimization](https://mlsanity.com/paper/2409.01163/) (2024)
- [Formal Verification of Unknown Dynamical Systems via Gaussian Process Regression](https://mlsanity.com/paper/2201.00655/) (2021)
- [Optimal uncertainty bounds for multivariate kernel regression under bounded noise: A Gaussian process-based dual function](https://mlsanity.com/paper/2603.16481/) (2026)
- [Transfer Learning for Control Systems via Neural Simulation Relations](https://mlsanity.com/paper/2412.01783/) (2024)
- [Data-Driven Synthesis of Probabilistic Controlled Invariant Sets for Linear MDPs](https://mlsanity.com/paper/2604.02727/) (2026)
- [On Uniform Error Bounds for Kernel Regression under Non-Gaussian Noise](https://mlsanity.com/paper/2605.09757/) (2026)
- [Asynchronous Cooperative Online Learning for Multi-Robot Control under Computational Delays](https://mlsanity.com/paper/2608.29562/) (2026)
- [Event-triggered Control and Online Learning for Networked Systems under Computational Delays](https://mlsanity.com/paper/2608.29576/) (2026)
- [COIN-GP: Cooperative Online Learning in Networked Distributed Systems with Partial Measurements via Gaussian Process Regression](https://mlsanity.com/paper/2609.20598/) (2026)

## Abstract (arXiv)

Symbolic models or abstractions are known to be powerful tools for the control design of cyber-physical systems (CPSs) with logic specifications. In this paper, we investigate a novel learning-based approach to the construction of symbolic models for nonlinear control systems. In particular, the symbolic model is constructed based on learning the un-modeled part of the dynamics from training data based on state-space exploration, and the concept of an alternating simulation relation that represents behavioral relationships with respect to the original control system. Moreover, we aim at achieving safe exploration, meaning that the trajectory of the system is guaranteed to be in a safe region for all times while collecting the training data. In addition, we provide some techniques to reduce the computational load, in terms of memory and computation time, of constructing the symbolic models and the safety controller synthesis, so as to make our approach practical. Finally, a numerical simulation illustrates the effectiveness of the proposed approach.