# A Barrier Certificate-based Simplex Architecture for Systems with Approximate and Hybrid Dynamics

arXiv: https://arxiv.org/abs/2202.09710 · HTML: https://mlsanity.com/paper/2202.09710/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 43 references that are in the map.
- First posted on arXiv 20 Feb 2022.

## Builds on (most cited first, 10 of 10)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Continuous control with deep reinforcement learning](https://mlsanity.com/paper/1509.02971/) (2015)
- [Concrete Problems in AI Safety](https://mlsanity.com/paper/1606.06565/) (2016)
- [Robust Deep Reinforcement Learning with Adversarial Attacks](https://mlsanity.com/paper/1712.03632/) (2017)
- [Neural Simplex Architecture](https://mlsanity.com/paper/1908.00528/) (2019)
- [Permissive Barrier Certificates for Safe Stabilization Using Sum-of-squares](https://mlsanity.com/paper/1802.08917/) (2018)
- [Data-driven verification and synthesis of stochastic systems via barrier certificates](https://mlsanity.com/paper/2111.10330/) (2021)
- [Dynamic-Weighted Simplex Strategy for Learning Enabled Cyber Physical Systems](https://mlsanity.com/paper/1902.02432/) (2019)
- [A Distributed Simplex Architecture for Multi-Agent Systems](https://mlsanity.com/paper/2012.10153/) (2020)
- [Distributed Barrier Certificates for Safe Operation of Inverter-Based Microgrids](https://mlsanity.com/paper/1903.09743/) (2019)

## Abstract (arXiv)

We present Barrier-based Simplex (Bb-Simplex), a new, provably correct design for runtime assurance of continuous dynamical systems. Bb-Simplex is centered around the Simplex control architecture, which consists of a high-performance advanced controller that is not guaranteed to maintain safety of the plant, a verified-safe baseline controller, and a decision module that switches control of the plant between the two controllers to ensure safety without sacrificing performance. In Bb-Simplex, Barrier certificates are used to prove that the baseline controller ensures safety. Furthermore, Bb-Simplex features a new automated method for deriving, from the barrier certificate, the conditions for switching between the controllers. Our method is based on the Taylor expansion of the barrier certificate and yields computationally inexpensive switching conditions. We also propose extensions to Bb-Simplex to enable its use in hybrid systems, which have multiple modes each with its own dynamics, and to support its use when only approximate dynamics (not exact dynamics) are available, for both continuous-time and hybrid dynamical systems. We consider significant applications of Bb-Simplex to microgrids featuring advanced controllers in the form of neural networks trained using reinforcement learning. These microgrids are modeled in RTDS, an industry-standard high-fidelity, real-time power systems simulator. Our results demonstrate that Bb-Simplex can automatically derive switching conditions for complex continuous-time and hybrid systems, the switching conditions are not overly conservative, and Bb-Simplex ensures safety even in the presence of adversarial attacks on the neural controller when only approximate dynamics (with an error bound) are available.