Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
162 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Safe Control Synthesis for Hybrid Systems through Local Control Barrier Functions (2311.17201v1)

Published 28 Nov 2023 in cs.SY, cs.RO, and eess.SY

Abstract: Control Barrier Functions (CBF) have provided a very versatile framework for the synthesis of safe control architectures for a wide class of nonlinear dynamical systems. Typically, CBF-based synthesis approaches apply to systems that exhibit nonlinear -- but smooth -- relationship in the state of the system and linear relationship in the control input. In contrast, the problem of safe control synthesis using CBF for hybrid dynamical systems, i.e., systems which have a discontinuous relationship in the system state, remains largely unexplored. In this work, we build upon the progress on CBF-based control to formulate a theory for safe control synthesis for hybrid dynamical systems. Under the assumption that local CBFs can be synthesized for each mode of operation of the hybrid system, we show how to construct CBF that can guarantee safe switching between modes. The end result is a switching CBF-based controller which provides global safety guarantees. The effectiveness of our proposed approach is demonstrated on two simulation studies.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (42)
  1. Control barrier function based quadratic programs for safety critical systems. IEEE Transactions on Automatic Control, 62(8):3861–3876, 2016.
  2. Learning control barrier functions from expert demonstrations. In 2020 59th IEEE Conference on Decision and Control (CDC), pages 3717–3724. IEEE, 2020.
  3. Differentiable safe controller design through control barrier functions. IEEE Control Systems Letters, 7:1207–1212, 2022.
  4. Learning adaptive safety for multi-agent systems. arXiv preprint arXiv:2309.10657, 2023.
  5. A game theoretic approach to controller design for hybrid systems. Proceedings of the IEEE, 88(7):949–970, 2000.
  6. Hamilton-jacobi reachability: A brief overview and recent advances. In 2017 IEEE 56th Annual Conference on Decision and Control (CDC), pages 2242–2253. IEEE, 2017.
  7. Computing controlled invariant sets for hybrid systems with applications to model-predictive control. IFAC-PapersOnLine, 51(16):193–198, 2018.
  8. Learning hybrid control barrier functions from data. In Conference on Robot Learning, pages 1351–1370. PMLR, 2021.
  9. Learning robust hybrid control barrier functions for uncertain systems. IFAC-PapersOnLine, 54(5):1–6, 2021.
  10. N. Athanasopoulos and R. Jungers. Combinatorial methods for invariance and safety of hybrid systems. Automatica, 98:130–140, 2018.
  11. S. Prajna and A. Jadbabaie. Safety verification of hybrid systems using barrier certificates. In International Workshop on Hybrid Systems: Computation and Control, pages 477–492. Springer, 2004.
  12. Verisig: verifying safety properties of hybrid systems with neural network controllers. In Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control, pages 169–178, 2019.
  13. Probabilistic reachability and safety for controlled discrete time stochastic hybrid systems. Automatica, 44(11):2724–2734, 2008.
  14. Hybrid nonsmooth barrier functions with applications to provably safe and composable collision avoidance for robotic systems. IEEE Robotics and Automation Letters, 4(2):1303–1310, 2019.
  15. M. Maghenem and R. G. Sanfelice. Characterizations of safety in hybrid inclusions via barrier functions. In Proceedings of the 22nd ACM International Conference on Hybrid Systems: Computation and Control, pages 109–118, 2019.
  16. A. Bisoffi and D. V. Dimarogonas. A hybrid barrier certificate approach to satisfy linear temporal logic specifications. In 2018 Annual American Control Conference (ACC), pages 634–639. IEEE, 2018.
  17. Safety barrier certificates for stochastic hybrid systems. In 2022 American Control Conference (ACC), pages 880–885. IEEE, 2022.
  18. Safe perception-based control under stochastic sensor uncertainty using conformal prediction. arXiv preprint arXiv:2304.00194, 2023.
  19. Adaptive safety using control barrier functions and hybrid adaptation. In 2021 American Control Conference (ACC), pages 2418–2423. IEEE, 2021.
  20. Perspectives and results on the stability and stabilizability of hybrid systems. Proceedings of the IEEE, 88(7):1069–1082, 2000.
  21. Learning lyapunov functions for hybrid systems. In Proceedings of the 24th International Conference on Hybrid Systems: Computation and Control, pages 1–11, 2021.
  22. D. Liberzon. Switching in systems and control, volume 190. Springer, 2003.
  23. Hybrid dynamical systems. IEEE control systems magazine, 29(2):28–93, 2009.
  24. M. S. Branicky. Multiple lyapunov functions and other analysis tools for switched and hybrid systems. IEEE Transactions on automatic control, 43(4):475–482, 1998.
  25. J. P. Hespanha. Uniform stability of switched linear systems: Extensions of lasalle’s invariance principle. IEEE transactions on Automatic Control, 49(4):470–482, 2004.
  26. H. Lin and P. J. Antsaklis. Stability and stabilizability of switched linear systems: a survey of recent results. IEEE Transactions on Automatic control, 54(2):308–322, 2009.
  27. Analysis and design of switched normal systems. Nonlinear Analysis: Theory, Methods & Applications, 65(12):2248–2259, 2006.
  28. H. Sun and J. Zhao. Control lyapunov functions for switched control systems. In Proceedings of the 2001 American Control Conference.(Cat. No. 01CH37148), volume 3, pages 1890–1891. IEEE, 2001.
  29. Safe Autonomy with Control Barrier Functions: Theory and Applications. Springer Nature, 2023.
  30. A. Clark. Verification and synthesis of control barrier functions. In 2021 60th IEEE Conference on Decision and Control (CDC), pages 6105–6112. IEEE, 2021.
  31. Permissive barrier certificates for safe stabilization using sum-of-squares. In 2018 Annual American Control Conference (ACC), pages 585–590. IEEE, 2018.
  32. Set propagation techniques for reachability analysis. Annual Review of Control, Robotics, and Autonomous Systems, 4(1):369–395, 2021.
  33. Safety-critical control and planning for obstacle avoidance between polytopes with control barrier functions. In 2022 International Conference on Robotics and Automation (ICRA), pages 286–292. IEEE, 2022.
  34. S. Boyd and L. Vandenberghe. Convex Optimization. Cambridge University Press, 2004.
  35. A. B. Kurzhanski and P. Varaiya. Ellipsoidal techniques for reachability analysis: internal approximation. Systems & control letters, 41(3):201–211, 2000.
  36. Parallelotope bundles for polynomial reachability. In Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control, pages 297–306, 2016.
  37. Convex optimization of nonlinear feedback controllers via occupation measures. The International Journal of Robotics Research, 33(9):1209–1230, 2014.
  38. S. Tonkens and S. Herbert. Refining control barrier functions through hamilton-jacobi reachability. In 2022 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS), pages 13355–13362. IEEE, 2022.
  39. Robust control barrier–value functions for safety-critical control. In 2021 60th IEEE Conference on Decision and Control (CDC), pages 6814–6821. IEEE, 2021.
  40. X. Tan and D. V. Dimarogonas. Compatibility checking of multiple control barrier functions for input constrained systems. In 2022 IEEE 61st Conference on Decision and Control (CDC), pages 939–944. IEEE, 2022.
  41. J. Breeden and D. Panagou. Compositions of multiple control barrier functions under input constraints. In 2023 American Control Conference (ACC), pages 3688–3695. IEEE, 2023.
  42. M. Black and D. Panagou. Consolidated control barrier functions: Synthesis and online verification via adaptation under input constraints. arXiv preprint arXiv:2304.01815, 2023.
Citations (2)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets