A journal of IEEE and CAA , publishes high-quality papers in English on original theoretical/experimental research and development in all areas of automation
Volume 9 Issue 11
Nov.  2022

IEEE/CAA Journal of Automatica Sinica

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Article Contents
Z. R. Zhu, Y. Chai, Z. M. Yang, and C. H. Huang, “Exponential-alpha safety criteria of a class of dynamic systems with barrier functions,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 11, pp. 1939–1951, Nov. 2022. doi: 10.1109/JAS.2020.1003408
 Citation: Z. R. Zhu, Y. Chai, Z. M. Yang, and C. H. Huang, “Exponential-alpha safety criteria of a class of dynamic systems with barrier functions,” IEEE/CAA J. Autom. Sinica, vol. 9, no. 11, pp. 1939–1951, Nov. 2022.

# Exponential-Alpha Safety Criteria of a Class of Dynamic Systems With Barrier Functions

##### doi: 10.1109/JAS.2020.1003408
Funds:  This work was supported by the National Natural Science Foundation of China (61633005)
• A classic kind of researches about the operational safety criterion for dynamic systems with barrier function can be roughly summarized as functional relationship, denoted by $\oplus$, between the barrier function and its first derivative for time t, where $\oplus$ can be “=”, “$<$”, or “$>$”, etc. This article draws on the form of the stable condition expression for finite time stability to formulate a novel kind of relaxed safety judgement criteria called exponential-alpha safety criteria. Moreover, we initially explore to use the control barrier function under exponential-alpha safety criteria to achieve the control for the dynamic system operational safety. In addition, derived from the actual process systems, we propose multi-hypersphere methods which are used to construct barrier functions and improved them for three types of special spatial relationships between the safe state set and the unsafe state set, where both of them can be spatially divided into multiple subsets. And the effectiveness of the proposed safety criteria are demonstrated by simulation examples.

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###### 通讯作者: 陈斌, bchen63@163.com
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沈阳化工大学材料科学与工程学院 沈阳 110142

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## Highlights

• We proposed a novel safety criterion called Exponential-alpha safety criterion, where the alpha belongs to positive real number field, in order to establish a weaker condition applied to improve a kind of safety criteria based on barrier functions and help to achieve safety control for a variety of actual dynamic systems
• Based on the Exponential-alpha safety criterion, we proposed a new control barrier function and then designed a safety controller for a classic kind of dynamic control systems
• We have enriched the Hypersphere Method Theory which can be used to construct the barrier functions for the dynamic system unsafe sets with complex connected, non-convex, and multiple sets. Then, we proposed Positive Multi-hypersphere Method and Reverse Multi-hypersphere Method

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