# Safe Control Algorithms Using Energy Functions: A Unified Framework, Benchmark, and New Directions

arXiv: https://arxiv.org/abs/1908.01883 · HTML: https://mlsanity.com/paper/1908.01883/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 Aug 2019.

## Built on by (most cited first, 17 of 17)

- [State-wise Safe Reinforcement Learning: A Survey](https://mlsanity.com/paper/2302.03122/) (2023)
- [Joint Synthesis of Safety Certificate and Safe Control Policy using Constrained Reinforcement Learning](https://mlsanity.com/paper/2111.07695/) (2021)
- [Safe Control with Neural Network Dynamic Models](https://mlsanity.com/paper/2110.01110/) (2021)
- [Constraint-Conditioned Policy Optimization for Versatile Safe Reinforcement Learning](https://mlsanity.com/paper/2310.03718/) (2023)
- [AutoCost: Evolving Intrinsic Cost for Zero-violation Reinforcement Learning](https://mlsanity.com/paper/2301.10339/) (2023)
- [Stable and Safe Reinforcement Learning via a Barrier-Lyapunov Actor-Critic Approach](https://mlsanity.com/paper/2304.04066/) (2023)
- [Safety Filters for Black-Box Dynamical Systems by Learning Discriminating Hyperplanes](https://mlsanity.com/paper/2402.05279/) (2024)
- [Safe Reinforcement Learning with Dual Robustness](https://mlsanity.com/paper/2309.06835/) (2023)
- [ModelVerification.jl: a Comprehensive Toolbox for Formally Verifying Deep Neural Networks](https://mlsanity.com/paper/2407.01639/) (2024)
- [Real-Time Safe Control of Neural Network Dynamic Models with Sound Approximation](https://mlsanity.com/paper/2404.13456/) (2024)
- [Verifiable Safety Q-Filters via Hamilton-Jacobi Reachability and Multiplicative Q-Networks](https://mlsanity.com/paper/2506.15693/) (2025)
- [Learn Zero-Constraint-Violation Policy in Model-Free Constrained Reinforcement Learning](https://mlsanity.com/paper/2111.12953/) (2021)
- [Safe and Sample-efficient Reinforcement Learning for Clustered Dynamic Environments](https://mlsanity.com/paper/2303.14265/) (2023)
- [A Lightweight and Transferable Design for Robust LEGO Manipulation](https://mlsanity.com/paper/2309.02354/) (2023)
- [Meta-Control: Automatic Model-based Control Synthesis for Heterogeneous Robot Skills](https://mlsanity.com/paper/2405.11380/) (2024)
- [Provably Safe, Yet Scalable Reinforcement Learning](https://mlsanity.com/paper/2606.14536/) (2026)
- [Safety Reinforced Model Predictive Control (SRMPC): Improving MPC with Reinforcement Learning for Motion Planning in Autonomous Driving](https://mlsanity.com/paper/2512.03774/) (2025)

## Abstract (arXiv)

Safe autonomy is important in many application domains, especially for applications involving interactions with humans. Existing safe control algorithms are similar to one another in the sense that: they all provide control inputs to maintain a low value of an energy function that measures safety. In different methods, the energy function is called a potential function, a safety index, or a barrier function. The connections and relative advantages among these methods remain unclear. This paper introduces a unified framework to derive safe control laws using energy functions. We demonstrate how to integrate existing controllers based on potential field method, safe set algorithm, barrier function method, and sliding mode algorithm into this unified framework. In addition to theoretical comparison, this paper also introduces a benchmark which implements and compares existing methods on a variety of problems with different system dynamics and interaction modes. Based on the comparison results, a new method, called the sublevel safe set algorithm, is derived under the unified framework by optimizing the hyperparameters. The proposed algorithm achieves the best performance in terms of safety and efficiency on the vast majority of benchmark tests.