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Volume 9 Issue 11
Nov.  2022

IEEE/CAA Journal of Automatica Sinica

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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. doi: 10.1109/JAS.2020.1003408

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)
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  • 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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    Y. Chai, K. Zhang, Y. F. Mao, and S. B. Wei. Analysis and Technology of Dynamic System Operational Safety. Beijing, China: Chemical Industry Press, 2019.
    Y. Chai, W. B. Mao, H. Ren, J. F. Qu, H. P. Yin, Z. M. Yang, L. Feng, B. S. Zhang, and X. Ye, “Research on operational safety assessment for spacecraft launch system: Progress and challenges,” Acta Automatica Sinica, vol. 45, pp. 1829–1845, Oct. 2019.
    S. Kabir, “An overview of fault tree analysis and its application in model based dependability analysis,” Expert Systems With Applications, vol. 77, pp. 114–135, Jul. 2017. doi: 10.1016/j.eswa.2017.01.058
    M. Talebberrouane, F. Khan, and Z. Lounis, “Availability analysis of safety critical systems using advanced fault tree and stochastic Petri net formalisms,” J. Loss Prevention in the Process Industries, vol. 44, pp. 193–203, Nov. 2016. doi: 10.1016/j.jlp.2016.09.007
    G. Landucci, A. Necci, G. Antonioni, F. Argenti, and V. Cozzani, “Risk assessment of mitigated domino scenarios in process facilities,” Reliability Engineering and System Safety, vol. 160, pp. 37–53, Apr. 2017. doi: 10.1016/j.ress.2016.11.023
    J. Nakayama, H. Misono, J. Sakamoto, J. Sakamoto, N. Kasai, T. Shibutani, and A. Miyake, “Simulationbased safety investigation of a hydrogen fueling station with an on-site hydrogen production system involving methylcyclohexane,” Int. J. Hydrogen Energy, vol. 42, pp. 10636–10644, Apr. 2017. doi: 10.1016/j.ijhydene.2016.11.072
    G. L. Li, Z. J. Zhou, C. H. Hu, L. L. Chang, Z. G. Zhou, and F. J. Zhao, “A new safety assessment model for complex system based on the conditional generalized minimum variance and the belief rule base,” Safety Science, vol. 93, pp. 108–120, Mar. 2017. doi: 10.1016/j.ssci.2016.11.011
    Y. Q. Chong, Z. F. Han, and X. Y. Zou, “Online assessment of complex industrial processes operating performance based on improved dynamic causality diagram,” Control Theory and Applications, vol. 34, pp. 345–354, Mar. 2017.
    M. A. v. Staalduinen, F. Khan, V. Gadag, and G. Reniers, “Functional quantitative security risk analysis (QSRA) to assist in protecting critical process infrastructure,” Reliability Engineering and System Safety, vol. 157, pp. 23–34, Jan. 2017. doi: 10.1016/j.ress.2016.08.014
    J. S. Busby, B. Green, and D. Hutchison, “Analysis of affordance, time, and adaptation in the assessment of industrial control system cybersecurity risk,” Risk Analysis, vol. 37, pp. 1298–1314, Jul. 2017. doi: 10.1111/risa.12681
    F. J. Zhao, Z. J. Zhou, C. H. Hu, L. L. Chang, and L. Wang, “Online safety assessment method based on evidential reasoning for dynamic systems,” Acta Autom. Sinica, vol. 43, pp. 1950–1961, Nov. 2017.
    R. Madigan, D. Golightly, and R. Madders, “Application of human factors analysis and classification system (HFACS) to UK rail safety of the line incidents,” Accident Analysis and Prevention, vol. 97, pp. 122–131, Dec. 2016. doi: 10.1016/j.aap.2016.08.023
    S. Prajna and A. Rantzer. “On the necessity of barrier certificates,” in Proc. IFAC World Congress, Prague, Czech, Jun. 2005, pp.526–531.
    S. Prajna, A. Jadbabaie, and G. J. Pappas. “Stochastic safety verification using barrier certificates,” in Proc. IEEE Conf. Decision and Control, Nassau, Bahamas, Dec. 2004.
    G. B. Wang, J. Liu, H. Y. Sun, J. Liu, and M. M. Zhang, “Safety verification of state/time-driven hybrid systems using barrier certificates,” in Proc. 35th Chinese Control Conf., Chengdu, China, Jul. 2016, pp. 2483–2489.
    H. Kong, X. Song, D. Han, M. Gu, and J. Sun, “A new barrier certificate for safety verification of hybrid systems,” Computer J., vol. 57, pp. 1033–1045, Jul. 2014. doi: 10.1093/comjnl/bxt059
    M. Z. Romdlony and B. Jayawardhana, “Stabilization with guaranteed safety using control lyapunov-barrier function,” Automatica, vol. 66, pp. 39–47, Apr. 2016. doi: 10.1016/j.automatica.2015.12.011
    G. B. Wang, J. F. He, J. Liu, H. Y. Sun, Z. H. Ding, and M. M. Zhao, “Safety verification of interconnected hybrid systems using barrier certificates,” Mathematical Problems in Engineering, pp.1–10, Mar. 2016.
    Z. R. Zhu, Yi Chai, and Z. M. Yang. “A novel kind of sufficient conditions for safety criterion based on control barrier function,” SCIENCE CHINA Information Sciences, vol.64, p.199205, Sept. 2021.
    A. D. Ames, J. W. Grizzle, and P. Tabuada. “Control barrier function based quadratic programs with application to adaptive cruise control,” in Proc. Decision and Control, IEEE 53rd Annual Conf., Los Angeles, USA, Dec. 2014, pp. 6271–6278.
    X. Xu, P. Tabuada, J. W. Grizzle, and A. D. Ames, “Robustness of control barrier functions for safety critical control,” IFAC Papers Online, vol. 48, pp. 54–61, Jun. 2015.
    P. Glotfelter, J. Corts, and M. Egerstedt, “Nonsmooth barrier functions with applications to multi-robot systems,” IEEE Control Syst. Lett., vol. 1, pp. 310–315, Jun. 2017. doi: 10.1109/LCSYS.2017.2710943
    U. Borrmann, L. Wang, A. D. Ames, and M. Egerstedt, “Control barrier certificates for safe swarm behavior,” IFAC Papers Online, vol. 48, pp. 68–73, Jun. 2015.
    L. Wang, A. D. Ames, and M. Egerstedt, “Safety barrier certificates for collisions-free multirobot systems,” IEEE Trans. Robot., vol. 33, pp. 661–674, Feb. 2017. doi: 10.1109/TRO.2017.2659727
    L. Wang, A. Ames, and M. Egerstedt. “Safety barrier certificates for heterogeneous multi-robot systems,” in Proc. American Control Conf., Boston, USA, 2016, pp.5213–5218.
    A. D. Ames, X. Xu, J. W. Grizzle, and P. Tabuada, “Control barrier function based quadratic programs for safety critical systems,” IEEE Trans. Autom. Control, vol. 62, pp. 3861–3876, Aug. 2017. doi: 10.1109/TAC.2016.2638961
    A. Agrawal and K. Sreenath. “Discrete control barrier functions for safety critical control of discrete systems with application to bipedal robot navigation,” in Proc. Robot. Sci. Syst., Cambridge, USA, Jul. 2017.
    S. P. Bhat and D. S. Bernstein, “Finite-time stability of continuous autonomous systems,” SIAM J. Control Optim., vol. 38, pp. 751–766, Mar. 2000. doi: 10.1137/S0363012997321358


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    • 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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