Skip to main content
SpringerLink
Log in

Safety criteria based on barrier function under the framework of boundedness for some dynamic systems

  • Research Paper
  • Published:
Science China Information Sciences Aims and scope Submit manuscript

Abstract

Barrier functions have been reported to be useful in quantifying the safety of some dynamic systems. Usually, when using the barrier functions, we try to transform safety analysis issues of dynamic systems into a class of reachability issues from a safe set to an unsafe set. This article presents a novel sufficient safety criterion for some dynamic systems. The proposed criterion is based on the barrier function and works as long as the upper bound of the barrier function is kept non-positive. Further, we present a mathematical description of fault safety for some dynamic system that experienced a fault at a certain time and propose a corresponding fault safety criterion for the aforementioned system.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Chai Y, Zhang K, Mao Y F, et al. Technology of Dynamic System Operational Safety (in Chinese). Beijing: Chemical Industry Press, 2019

    Google Scholar 

  2. Chai Y, Mao W B, Ren H, et al. Research on operational safety assessment for spacecraft launch system: progress and challenges (in Chinese). Acta Autom Sin, 2019, 45: 1829–1845

    Google Scholar 

  3. Bouamama B O, Biswas G, Loureiro R, et al. Graphical methods for diagnosis of dynamic systems: review. Annu Rev Control, 2014, 38: 199–219

    Article  Google Scholar 

  4. Kasai N, Fujimoto Y, Yamashita I, et al. The qualitative risk assessment of an electrolytic hydrogen generation system. Int J Hydrogen Energy, 2016, 41: 13308–13314

    Article  Google Scholar 

  5. Cunha S B. A review of quantitative risk assessment of onshore pipelines. J Loss Prevent Process Ind, 2016, 44: 282–298

    Article  Google Scholar 

  6. Ahn J, Chang D. Fuzzy-based HAZOP study for process industry. J Hazard Mater, 2016, 317: 303–311

    Article  Google Scholar 

  7. Chang Y Q, Han Z F, Zou X T. Online assessment of complex industrial processes operating performance based on improved dynamic causality diagram (in Chinese). Control Theory Appl, 2017, 34: 345–354

    Google Scholar 

  8. Khan F, Hashemi S J, Paltrinieri N, et al. Dynamic risk management: a contemporary approach to process safety management. Curr Opin Chem Eng, 2016, 14: 9–17

    Article  Google Scholar 

  9. Naderpour M, Lu J, Zhang G Q. An abnormal situation modeling method to assist operators in safety-critical systems. Reliab Eng Syst Saf, 2015, 133: 33–47

    Article  Google Scholar 

  10. Villa V, Paltrinieri N, Khan F, et al. Towards dynamic risk analysis: a review of the risk assessment approach and its limitations in the chemical process industry. Saf Sci, 2016, 89: 77–93

    Article  Google Scholar 

  11. Busby J S, Green B, Hutchison D. Analysis of affordance, time, and adaptation in the assessment of industrial control system cybersecurity risk. Risk Anal, 2017, 37: 1298–1314

    Article  Google Scholar 

  12. Li H T. Research on safety analysis method based on safety risk state (in Chinese). Dissertation for Ph.D. Degree. Changsha: National University of Defense Technology, 2012

    Google Scholar 

  13. Kriaa S, Pietre-Cambacedes L, Bouissou M, et al. A survey of approaches combining safety and security for industrial control systems. Reliab Eng Syst Saf, 2015, 139: 156–178

    Article  Google Scholar 

  14. Talebberrouane M, Khan F, Lounis Z. Availability analysis of safety critical systems using advanced fault tree and stochastic Petri net formalisms. J Loss Prevent Process Ind, 2016, 44: 193–203

    Article  Google Scholar 

  15. Guo Y B, Meng X L, Wang D G, et al. Comprehensive risk evaluation of long-distance oil and gas transportation pipelines using a fuzzy Petri net model. J Nat Gas Sci Eng, 2016, 33: 18–29

    Article  Google Scholar 

  16. Wang X, Mahulea C, Silva M. Diagnosis of time Petri nets using fault diagnosis graph. IEEE Trans Autom Control, 2015, 60: 2321–2335

    Article  MathSciNet  MATH  Google Scholar 

  17. Landucci G, Argenti F, Cozzani V, et al. Assessment of attack likelihood to support security risk assessment studies for chemical facilities. Process Saf Environ Protection, 2017, 110: 102–114

    Article  Google Scholar 

  18. Barua S, Gao X D, Pasman H, et al. Bayesian network based dynamic operational risk assessment. J Loss Prevention Process Ind, 2016, 41: 399–410

    Article  Google Scholar 

  19. Ye L B. A study on operation safety analysis and online assessment of industrial processes (in Chinese). Dissertation for Ph.D. Degree. Hangzhou: Zhejiang University, 2011

    Google Scholar 

  20. Romdlony M Z, Jayawardhana B. Stabilization with guaranteed safety using control Lyapunov-barrier function. Automatica, 2016, 66: 39–47

    Article  MathSciNet  MATH  Google Scholar 

  21. Prajna S, Rantzer A. On the necessity of barrier certificates. In: Proceedings of the 16th IFAC World Congress, Prague, 2005. 526–531

  22. Prajna S, Jadbabaie A, Pappas G J. Stochastic safety verification using barrier certificates. In: Proceedings of IEEE Conference on Decision and Control, 2004

  23. Kong H, Song X Y, Han D, et al. A new barrier certificate for safety verification of hybrid systems. Comput J, 2014, 57: 1033–1045

    Article  Google Scholar 

  24. Wang G B, He J F, Liu J, et al. Safety verification of interconnected hybrid systems using barrier certificates. Math Problem Eng, 2016, 2016: 1–10

    MathSciNet  MATH  Google Scholar 

  25. Wang G B, Liu J, Sun H Y, et al. Safety verification of state/time-driven hybrid systems using barrier certificates. In: Proceedings of the 35th Chinese Control Conference (CCC), 2016. 2483–2489

  26. Zhu Z R, Chai Y, Yang Z M. A novel kind of sufficient conditions for safety judgement based on control barrier function. Sci China Inf Sci, 2021, 64: 199205

    Article  MathSciNet  Google Scholar 

  27. Ames A D, Grizzle J W, Tabuada P. Control barrier function based quadratic programs with application to adaptive cruise control. In: Proceedings of the 53rd Annual Conference on Decision and Control (CDC), 2014. 6271–6278

  28. Xu X R, Tabuada P, Grizzle J W, et al. Robustness of control barrier functions for safety critical control. IFAC-PapersOnLine, 2015, 48: 54–61

    Article  Google Scholar 

  29. Glotfelter P, Cortes J, Egerstedt M. Nonsmooth barrier functions with applications to multi-robot systems. IEEE Control Syst Lett, 2017, 1: 310–315

    Article  MathSciNet  Google Scholar 

  30. Borrmann U, Wang L, Ames A D, et al. Control barrier certificates for safe swarm behavior. IFAC-PapersOnLine, 2015, 48: 68–73

    Article  Google Scholar 

  31. Wang L, Ames A D, Egerstedt M. Safety barrier certificates for collisions-free multirobot systems. IEEE Trans Robot, 2017, 33: 661–674

    Article  Google Scholar 

  32. Wang L, Ames A, Egerstedt M. Safety barrier certificates for heterogeneous multi-robot systems. In: Proceedings of American Control Conference (ACC), Boston, 2016. 5213–5218

  33. Ames A D, Xu X, Grizzle J W, et al. Control barrier function based quadratic programs for safety critical systems. IEEE Trans Autom Control, 2017, 62: 3861–3876

    Article  MathSciNet  MATH  Google Scholar 

  34. Agrawal A, Sreenath K. Discrete control barrier functions for safety critical control of discrete systems with application to bipedal robot navigation. In: Proceedings of Robotics: Science and Systems Conference, Cambridge, 2017

  35. Tong S C, Li Y M. Observer-based adaptive fuzzy backstepping control of uncertain nonlinear pure-feedback systems. Sci China Inf Sci, 2014, 57: 012204

    Article  MathSciNet  MATH  Google Scholar 

  36. Jain A K, Bhasin S. Tracking control of uncertain nonlinear systems with unknown constant input delay. IEEE/CAA J Autom Sin, 2020, 7: 420–425

    Article  MathSciNet  Google Scholar 

  37. Tong S C, Li Y M. Robust adaptive fuzzy backstepping output feedback tracking control for nonlinear system with dynamic uncertainties. Sci China Inf Sci, 2010, 53: 307–324

    Article  MathSciNet  MATH  Google Scholar 

  38. Gomes J P P, Galvao R K H, Yoneyama T, et al. A new degradation indicator based on a statistical anomaly approach. IEEE Trans Rel, 2016, 65: 326–335

    Article  Google Scholar 

  39. Zheng J F, Si X S, Hu C H, et al. A nonlinear prognostic model for degrading systems with three-source variability. IEEE Trans Rel, 2016, 65: 736–750

    Article  Google Scholar 

  40. Department of Mathematics, East China Normal University. Mathematical Analysis (in Chinese). 3rd. Beijing: Higher Education Press, 1999

    Google Scholar 

Download references

Acknowledgements

This work was supported by National Natural Science Foundation of China (Grant No. 61633005).

Author information

Authors and Affiliations

  1. State Key Laboratory of Power Transmission Equipment and System Security and New Technology, Chongqing University, Chongqing, 400044, China

    Zheren Zhu, Yi Chai & Chenghong Huang

  2. School of Automation, Chongqing University, Chongqing, 400044, China

    Zheren Zhu, Yi Chai & Chenghong Huang

  3. Chongqing High-Tech-Zone Feima Innovation Research Institute, Chongqing, 400050, China

    Zhimin Yang

Authors
  1. Zheren Zhu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yi Chai
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Zhimin Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Chenghong Huang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Yi Chai.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhu, Z., Chai, Y., Yang, Z. et al. Safety criteria based on barrier function under the framework of boundedness for some dynamic systems. Sci. China Inf. Sci. 65, 122203 (2022). https://doi.org/10.1007/s11432-020-3028-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s11432-020-3028-4

Keywords

Search

Navigation