On the Optimality, Stability, and Feasibility of Control Barrier Functions: An Adaptive Learning-Based Approach

• URL: http://arxiv.org/abs/2305.03608v1
• Date: Fri, 5 May 2023 15:11:28 GMT
• Title: On the Optimality, Stability, and Feasibility of Control Barrier Functions: An Adaptive Learning-Based Approach
• Authors: Alaa Eddine Chriat and Chuangchuang Sun
• Abstract summary: Control barrier function (CBF) and its variants have attracted extensive attention for safety-critical control. There are still fundamental limitations of current CBFs: optimality, stability, and feasibility. We propose Adaptive Multi-step Control Barrier Function (AM-CBF), where we parameterize the class-$mathcalK$ function by a neural network and train it together with the reinforcement learning policy.
• Score: 4.399563188884702
• License: http://creativecommons.org/licenses/by-nc-sa/4.0/
• Abstract: Safety has been a critical issue for the deployment of learning-based approaches in real-world applications. To address this issue, control barrier function (CBF) and its variants have attracted extensive attention for safety-critical control. However, due to the myopic one-step nature of CBF and the lack of principled methods to design the class-$\mathcal{K}$ functions, there are still fundamental limitations of current CBFs: optimality, stability, and feasibility. In this paper, we proposed a novel and unified approach to address these limitations with Adaptive Multi-step Control Barrier Function (AM-CBF), where we parameterize the class-$\mathcal{K}$ function by a neural network and train it together with the reinforcement learning policy. Moreover, to mitigate the myopic nature, we propose a novel \textit{multi-step training and single-step execution} paradigm to make CBF farsighted while the execution remains solving a single-step convex quadratic program. Our method is evaluated on the first and second-order systems in various scenarios, where our approach outperforms the conventional CBF both qualitatively and quantitatively.

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