Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
156 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

A Tunable Universal Formula for Safety-Critical Control (2403.06285v2)

Published 10 Mar 2024 in eess.SY, cs.SY, and math.OC

Abstract: Sontag's universal formula is a widely-used technique for stabilizing control through control Lyapunov functions, and it has been extended to address safety-critical control in recent years by incorporating control barrier functions (CBFs). However, how to derive a universal formula that satisfies requirements on essential properties, including safety, robustness, and smoothness, is still an open problem. To address this challenge, this paper introduces a novel solution - a tunable universal formula - by incorporating a (state-dependent) tunable scaling term into Sontag's universal formula. This tunable scaling term enables the regulation of safety control performances, allowing the attainment of desired properties through a proper selection. Furthermore, we extend this tunable universal formula to address safety-critical control problems with norm-bounded input constraints, showcasing its applicability across diverse control scenarios. Finally, we demonstrate the efficacy of our method through a collision avoidance example, investigating the essential properties including safety, robustness, and smoothness under various tunable scaling terms.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (20)
  1. G. O. Young, “Synthetic structure of industrial plastics,” in Plastics, 2nd ed., vol. 3, J. Peters, Ed. New York, NY, USA: McGraw-Hill, 1964, pp. 15–64.
  2. J. U. Duncombe, “Infrared navigation—Part I: An assessment of feasibility,” IEEE Trans. Electron Devices, vol. ED-11, no. 1, pp. 34–39, Jan. 1959, 10.1109/TED.2016.2628402.
  3. E. P. Wigner, “Theory of traveling-wave optical laser,” Phys. Rev., vol. 134, pp. A635–A646, Dec. 1965.
  4. E. H. Miller, “A note on reflector arrays,” IEEE Trans. Antennas Propagat., to be published.
  5. E. E. Reber, R. L. Michell, and C. J. Carter, “Oxygen absorption in the earth’s atmosphere,” Aerospace Corp., Los Angeles, CA, USA, Tech. Rep. TR-0200 (4230-46)-3, Nov. 1988.
  6. J. H. Davis and J. R. Cogdell, “Calibration program for the 16-foot antenna,” Elect. Eng. Res. Lab., Univ. Texas, Austin, TX, USA, Tech. Memo. NGL-006-69-3, Nov. 15, 1987.
  7. G. O. Young, “Synthetic structure of industrial plastics,” in Plastics, vol. 3, Polymers of Hexadromicon, J. Peters, Ed., 2nd ed. New York, NY, USA: McGraw-Hill, 1964, pp. 15-64. [Online]. Available: http://www.bookref.com.
  8. J. S. Turner, “New directions in communications,” IEEE J. Sel. Areas Commun., vol. 13, no. 1, pp. 11-23, Jan. 1995.
  9. W. P. Risk, G. S. Kino, and H. J. Shaw, “Fiber-optic frequency shifter using a surface acoustic wave incident at an oblique angle,” Opt. Lett., vol. 11, no. 2, pp. 115–117, Feb. 1986.
  10. R. J. Hijmans and J. van Etten, “Raster: Geographic analysis and modeling with raster data,” R Package Version 2.0-12, Jan. 12, 2012. [Online]. Available: http://CRAN.R-project.org/package=raster
  11. D. B. Payne and J. R. Stern, “Wavelength-switched pas- sively coupled single-mode optical network,” in Proc. IOOC-ECOC, Boston, MA, USA, 1985, pp. 585–590.
  12. D. Ebehard and E. Voges, “Digital single sideband detection for interferometric sensors,” presented at the 2nd Int. Conf. Optical Fiber Sensors, Stuttgart, Germany, Jan. 2-5, 1984.
  13. G. Brandli and M. Dick, “Alternating current fed power supply,” U.S. Patent 4 084 217, Nov. 4, 1978.
  14. J. O. Williams, “Narrow-band analyzer,” Ph.D. dissertation, Dept. Elect. Eng., Harvard Univ., Cambridge, MA, USA, 1993.
  15. N. Kawasaki, “Parametric study of thermal and chemical nonequilibrium nozzle flow,” M.S. thesis, Dept. Electron. Eng., Osaka Univ., Osaka, Japan, 1993.
  16. B. Smith, “An approach to graphs of linear forms,” unpublished.
  17. A. Brahms, “Representation error for real numbers in binary computer arithmetic,” IEEE Computer Group Repository, Paper R-67-85.
  18. Letter Symbols for Quantities, ANSI Standard Y10.5-1968.
  19. R. Fardel, M. Nagel, F. Nuesch, T. Lippert, and A. Wokaun, “Fabrication of organic light emitting diode pixels by laser-assisted forward transfer,” Appl. Phys. Lett., vol. 91, no. 6, Aug. 2007, Art. no. 061103. 
  20. J. Zhang and N. Tansu, “Optical gain and laser characteristics of InGaN quantum wells on ternary InGaN substrates,” IEEE Photon. J., vol. 5, no. 2, Apr. 2013, Art. no. 2600111

Summary

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

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