Minimum-seeking for CLFs: Universal semiglobally stabilizing feedback under unknown control directions

IEEE Transactions on Automatic Control

Volumn 58, Issue 5, 2013, Pages 1107-1122

  Scheinker, Alexander ^a,b   Krstić, Miroslav ^c  

^a LOS ALAMOS NATIONAL LABORATORY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Control Lyapunov functions (CLF); Extremum seeking (ES); Lie bracket averaging

Indexed keywords

CONTROL THEORY; COUPLINGS; LYAPUNOV METHODS; STABILIZATION;

CONTROL DIRECTIONS; CONTROL LYAPUNOV FUNCTION; EXTREMUM SEEKING; LIE BRACKETS; PARAMETRIC PERTURBATIONS; PRACTICAL STABILITY; TRANSIENT PERFORMANCE; UNKNOWN CONTROL DIRECTION;

CONTROLLERS;

EID: 84888219262     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2012.2225514     Document Type: Article

References (68)

1. V. Adetola and M. Guay, "Adaptive output feedback extremum seeking receding horizon control of linear systems," J. Process Control, vol. 16, pp. 521-533, 2006.
2. V. Adetola and M. Guay, "Guaranteed parameter convergence for extremum-seeking control of nonlinear systems," Automatica, vol. 43, pp. 105-110, 2007.
3. K. B. Ariyur and M. Krstic, Real-Time Optimization by Extremum-Seeking Control. Hoboken, NJ: Wiley-Interscience, 2003.
4. V. Arnold, Mathematical Methods of Classical Mechanics. Moscow, Russia: Nauka, 1974.
5. A. Banaszuk, K. B. Ariyur, M. Krstic, and C. A. Jacobson, "An adaptive algorithm for control of combustion instability," Automatica, vol. 40, pp. 1965-1972, 2004.
6. R. Becker, R. King, R. Petz, and W. Nitsche, "Adaptive closed-loop separation control on a high-lift configuration using extremum seeking," AIAA Paper 2006-3493 2006.
7. R. Becker, R. King, W. Petz, and W. Nitsche, "Adaptive closed-loop separation control on a high-lift configuration using extremum seeking," AIAA J., vol. 45, pp. 1382-1392.
8. A. Brunn, W. Nitsche, L. Henning, and R. King, "Application of Slope-Seeking to a Generic Car Model for Active Drag Control," preprint, 2012.
9. D. Carnevale, A. Astolfi, C. Centioli, S. Podda, V. Vitale, and L. Zaccarian, "A New Extremum Seeking Technique and Its Application to Maximize RF Heating on FTU," Fusing Eng. Design, vol. 84, pp. 554-558, 2009.
10. C. Centioli, F. Iannone, G. Mazza, M. Panella, L. Pangione, S. Podda, A. Tuccillo, V. Vitale, and L. Zaccarian, "Maximization of the lower hybrid power coupling in the Frascati Tokamak Upgrade via extremum seeking," Control Eng. Practice, vol. 16, pp. 1468-1478, 2008.
11. J.-Y. Choi, M. Krstic, K. B. Ariyur, and J. S. Lee, "Extremum seeking control for discrete-time systems," IEEE Trans. Autom. Control, vol. 47, pp. 318-323, 2002.
12. J. Cochran, E. Kanso, S. D. Kelly, H. Xiong, and M. Krstic, "Source seeking for two nonholonomic models of fish locomotion," IEEE Trans. Robotics, vol. 25, no. 5, pp. 1166-1176, 2009.
13. J. Cochran and M. Krstic, "Nonholonomic source seeking with tuning of angular velocity," IEEE Trans. Autom. Control, vol. 54, no. 4, pp. 717-731, Apr. 2009.
14. J. Creaby, Y. Li, Y., and J. E. Seem, "Maximizing wind turbine energy capture using multivariable extremum seeking control," Wind Eng., vol. 33, pp. 361-387, 2009.
15. D. DeHaan and M. Guay, "Extremum-seeking control of state-constrained nonlinear systems," Automatica, vol. 41, pp. 1567-1574, 2005.
16. Z. Ding, "Global adaptive output feedback stabilization of nonlinear systems of any relative degree with unknown high frequency gain," IEEE Trans. Auitom. Control, vol. 43, pp. 1442-1446, 1998.
17. H. Dürr, M. Stanković, and K. Johansson, "A lie bracket approximation for extremum seeking vehicles," in Proc. IFAC World Cong., Milan, 2011, [CD ROM].
18. H. Dürr, M. Stanković, and K. Johansson, "Nash Equilibrium Seeking in Multi-Vehicle Systems: A Lie Bracket Approximation-Based Approach," [Online]. Available: http://arxiv.org/abs/1109.6129 Nov. 17, 2011
19. A. Favache, M. Guay, M. Perrier, and D. Dochain, "Extremum seeking control of retention for a microparticulate system," Canadian J. Chem. Eng., vol. 86, pp. 815-827, 2008.
20. R. Freeman and P. Kokotović, Robust Nonlinear Control Design. Boston, MA: Birkhauser, 1996.
21. P. Frihauf, M. Krstic, and T. Başar, "Nash equilibrium seeking in noncooperative games," IEEE Trans. Autom. Control, vol. 57, pp. 1192-1207, 2012.
22. S. Ge, C. Yang, and T. Lee, "Adaptive robust control of a class of nonlinear strict-feedback discrete-time systems with unknown control directions," Syst. Control Lett., vol. 57, pp. 888-895, 2008.
23. M. Guay, D. Dochain, M. Perrier, and N. Hudon, "Flatness-based extremum-seeking control over periodic orbits," IEEE Trans. Automatic Control, vol. 52, pp. 2005-2012, 2007.
24. M. Guay, M. Perrier, and D. Dochain, "Adaptive extremum seeking control of nonisothermal continuous stirred reactors," Chem. Eng. Sci., vol. 60, pp. 3671-3681, 2005.
25. L. Gurvits, "Averaging approach to nonholonomic motion planning," in Proc. IEEE. Conf. Robot. Autom., Nice, France, May 1992, pp. 2541-2546.
26. L. Gurvits and Z. Li, "Smooth Time-Periodic Solutions for Non-Holonomic Motion Planning," NYU, Tech. Rep. TR-598, 1992.
27. L. Gurvits and Z. Li, "Smooth time-periodic solutions for non-holonomic motion planning," in Nonholonomic Motion Planning, Z. Li and J. F. Canny., Eds. Norwell, MA: Kluwer, 1992.
28. L. Henning, R. Becker, G. Feuerbach, R. Muminovic, A. Brunn, W. Nitsche, and R. King, "Extensions of adaptive slope-seeking for active flow control," J. Syst. Control Eng., vol. 222, no. 5, pp. 309-322, Aug. 2008.
29. P. Ioannou and J. Sun, Robust Adaptive Control. Englewood Cliffs, NJ: Prentice Hall, 1996.
30. J. Kaloust and Z. Qu, "Robust control design for nonlinear uncertain systems with an unknown time-varying control direction," IEEE Trans. Auitom. Control, vol. 42, pp. 393-399, 1997.
31. K. Kim, C. Kasnakoglu, A. Serrani, and M. Samimy, "Extremum-seeking control of subsonic cavity flow," AIAA J., vol. 47, pp. 195-205, 2009.
32. R. King, R. Becker, G. Feuerbach, L. Henning, R. Petz, W. Nitsche, O. Lemke, and W. Neise, "Adaptive flow control using slope seeking," in Proc. 14th IEEE Mediterranean Conf. Control Autom., Ancona, Italy, 2006, pp. 1-6.
33. M. Krstić and H. Deng, Stabilization of Nonlinear Uncertain Systems. New York: Springer-Verlag, 1998.
34. M. Krstić, I. Kanellakopoulos, and P. V. Kokotović, "Nonlinear and Adaptive Control Design," 1995.
35. M. Krstić and Z. Li, "Inverse optimal design of input-to-state stabilizing nonlinear controllers," IEEE Trans. Auitom. Control, vol. 43, pp. 336-350, 1998.
36. M. Krstić and H. Wang, "Stability of extremum seeking feedback for general dynamic systems," Automatica, vol. 36, pp. 595-601, 2000.
37. P. Lei, Y. Li, Q. Chen, and J. E. Seem, "Extremum seeking control based integration of MPPT and degradation detection for photovoltaic arrays," in Proc. Amer. Control Conf., 2010, [CD ROM].
38. P. Li, Y. Li, and J. E. Seem, "Efficient operation of air-side economizer using extremum seeking control," ASME Trans. - J. Dyn. Syst., Meas. Control, vol. 132, pp. 31-41, 2010.
39. Y. Li, M. A. Rotea, G. Chiu, L. Mongeau, and I. Paek, "Extremum seeking control of tunable thermoacoustic cooler," IEEE Trans. Control Syst. Technol., vol. 13, pp. 527-536, 2005.
40. L. Luo, E. Schuster, and M. Krstić, "MHD channel flow control in 2D: Mixing enhancement by boundary feedback," Automatica, vol. 44, pp. 2498-2507, 2008.
41. R. Marino and P. Tomei, "Robust stabilization of feedback linearizable time-varying uncertain nonlinear systems," Automatica, vol. 29, pp. 181-189, 1993.
42. B. Martensson, "Remarks on adaptive stabilization of first-order nonlinear systems," Syst. Control Lett., vol. 14, pp. 1-7, 1990.
43. W. H. Moase and C. Manzie, "Fast extremum - Seeking for Wiener-Hammerstein plants," Automatica, vol. 48, pp. 2433-2443, 2012.
44. W. H. Moase, C. Manzie, and M. J. Brear, "Newton-like extremum-seeking for the control of thermoacoustic instability," IEEE Trans. Autom. Control, vol. 55, pp. 2094-2105, 2010.
45. J. P. Moeck, M. R. Bothien, C. O. Paschereit, G. Gelbert, and R. King, "Two-parameter extremum seeking for control of thermoacoustic instabilities and characterization of linear growth," 2012, AIAA Paper 2007-1416.
46. L. Moreau and D. Aeyels, "Practical stability and stabilization," IEEE Trans. Auitom. Control, vol. 45, pp. 1554-1558, 2000.
47. D. Mudgett and S. Morse, "Adaptive stabilization of linear systems with unknown high-frequency gains," IEEE Trans. Auitom. Control, vol. 30, pp. 549-554, 1985.
48. D. Nešić, Y. Tan, W. H. Moase, and C. Manzie, "A unifying approach to extremum seeking: Adaptive schemes based on estimation of derivatives," in Proc. Conf. Dec. Control, Atlanta, GA, Dec. 2010, [CD ROM].
49. R. Nussbaum, "Some remarks on a conjecture in parameter adaptive control," Syst. Control Lett., vol. 3, pp. 243-246, 1985.
50. K. Peterson and A. Stefanopoulou, "Extremum seeking control for soft landing of an electromechanical valve actuator," Automatica, vol. 29, pp. 1063-1069, 2004.
51. M. A. Rotea, "Analysis of multivariable extremum seeking algorithms," in Proc. Amer. Control Conf., 2000, [CD ROM].
52. S. Sam and J. Wang, "Robust adaptive tracking for time-varying ucnertain nonlinear systems with unknown control coefficients," IEEE Trans. Auitom. Control, vol. 48, pp. 1463-1469, 2003.
53. R. Sepulchre, M. Jankovic, and P. V. Kokotović, Constructive Nonlinear Control. New York: Springer, 1997.
54. E. Sontag, "A "universal" construction of Artstein's theorem on nonlinear stabilization," Syst. Control Lett., vol. 13, pp. 117-123, 1989.
55. M. S. Stanković, K. H. Johansson, and D. M. Stipanović, "Distributed-seeking of Nash equilibria with applications to mobile sensor networks," IEEE Trans. Auitom. Control, vol. 57, pp. 904-919, 2012.
56. M. S. Stanković and D. M. Stipanović, "Extremum seeking under stochastic noise and applications to mobile sensors," Automatica, vol. 46, pp. 1243-1251, 2010.
57. Y. Tan, D. Nešić, and I. Mareels, "On non-local stability properties of extremum seeking control," Automatica, vol. 42, pp. 889-903, 2006.
58. P. Tomei and R. Marino, Nonlinear Control Design. London, U.K.: Prentice Hall, 1995.
59. H.-H. Wang and M. Krstic, "Extremum seeking for limit cycle minimization," IEEE Trans. Autom. Control, vol. 45, pp. 2432-2437, 2000.
60. H.-H. Wang, S. Yeung, and M. Krstic, "Experimental application of extremumseeking on an axial-flow compressor," IEEE Trans. Control Syst. Technol., vol. 8, pp. 300-309, 2000.
61. O. Wiederhold, L. Neuhaus, R. King, W. Niese, L. Enghardt, B. R. Noack, and M. Swoboda, "Extensions of extremum-seeking control to improve the aerodynamic performance of axial turbomachines," in Proc. 39th AIAA Fluid Dyn. Conf., San Antonio, TX, U.S.A., 2009, [CD ROM].
62. Y. Xudong, "Asymptotic regulation of time-varying uncertain nonlinear systems with unknown control directions," Automatica, vol. 35, pp. 929-935, 1999.
63. Y. Xudong and Z. Ding, "Robust tracking control of uncertain nonlinear systems with unknown control directions," Syst. Control Lett., vol. 42, pp. 1-10, 2001.
64. X. Ye and J. Jiang, "Adaptive nonlinear design without a priori knowledge of control directions," IEEE Trans. Auitom. Control, vol. 43, pp. 1617-1621, 1998.
65. C. Zhang, D. Arnold, N. Ghods, A. Siranosian, and M. Krstic, "Source seeking with nonholonomic unicycle without position measurement and with tuning of forward velocity," Syst. Control Lett., vol. 56, pp. 245-252, 2007.
66. X. T. Zhang, D. M. Dawson, W. E. Dixon, and B. Xian, "Extremum- seeking nonlinear controllers for a human exercise machine," IEEE/ASME Trans. Mechatron., vol. 11, pp. 233-240, 2006.
67. C. Zhang, A. Siranosian, and M. Krstić, "Extremum seeking for moderately unstable systems and for autonomous vehicle target tracking without position measurements," Automatica, vol. 43, pp. 1832-1839, 2007.
68. Y. Zhang, C. Wen, and Y. Soh, "Adaptive backstepping control design for systems with unknown high-frequency gain," IEEE Trans. Auitom. Control, vol. 45, pp. 2350-2354, 2000.