On non-local stability properties of extremum seeking control

Automatica

Volumn 42, Issue 6, 2006, Pages 889-903

  Tan, Ying ^a   Nešić, Dragan ^a   Mareels, Iven ^a  

^a UNIVERSITY OF MELBOURNE   (Australia)

Author keywords

Convergence speed; Domain of the attraction; Extremum seeking control; Semi global practical stability

Indexed keywords

CLOSED LOOP CONTROL SYSTEMS; COMPUTER SIMULATION; CONTROL EQUIPMENT; CONVERGENCE OF NUMERICAL METHODS; PARAMETER ESTIMATION;

CONVERGENCE SPEED; DOMAIN OF THE ATTRACTION; EXTREMUM SEEKING CONTROL; SEMI-GLOBAL PRACTICAL STABILITY;

SYSTEM STABILITY;

EID: 33646151136     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2006.01.014     Document Type: Article

References (28)

1. Christofides P.D., and Teel A.R. Singular perturbation & input-to-state stability. IEEE Transactions on Automatic Control 41 (1996) 1645-1650
2. Edwards C.H., and Penney D.E. Calculus with analytic geometry. (5th ed.) (1998), Prentice Hall, Upper Saddle River, New Jersey
3. Guay M., Dochain D., and Perrier M. Adaptive extremum seeking control of continuous stirred tank bioreactors with unknown growth kinetics. Automatica 40 (2004) 1645-1650
4. Guay M., and Zhang T. Adaptive extremum seeking control of nonlinear dynamic systems with parametric uncertainties. Automatica 39 (2003) 1283-1293
5. KHalil H.K. Nonlinear systems. (3rd ed.) (2002), Prentice-Hall, Upper Saddle River, New Jersey
6. Krstić M. Performance improvement & limitations in extremum seeking control. Systems and Control Letters 39 (2000) 313-326
7. Krstić M., and Wang H.H. Stability of extremum seeking feedback for general nonlinear dynamic systems. Automatica 36 (2000) 595-601
8. Lin, Y. (1992). Lyapunov function technique for stabilization. Ph.D. dissertation, Rutgers University.
9. Meerkov S.M. Asymptotic methods for investigating a class of forced states in extremal systems. Automatic and Remote Control 12 (1967) 1916-1920
10. Meerkov S.M. Asymptotic methods for investigating quasi-stationary states in continuous systems of automatic optimization. Automatic and Remote Control 11 (1967) 1726-1743
11. Meerkov S.M. Asymptotic methods for investigating quasi-stationary states in continuous systems of automatic optimization subject to disturbance action. Automatika i Telemekhanika 12 (1967) 14-24 (in Russian)
12. Morosanov I.S. Method of extremum control. Automatic and Remote Control 18 (1957) 1077-1092
13. Nešić D., and Teel A.R. Input-to-state stability for nonlinear time-varying systems via averaging. Mathematics of Control Signals and Systems 14 (2001) 524-533
14. Ortega J.M., and Rheinboldt W.C. Iterative solution of nonlinear equations in several variables (1970), Academic Press, New York
15. Ostrovskii I.I. Extremum regulation. Automatic and Remote Control 18 (1957) 900-907
16. Peterson K.S., and Stefanopoulou A.G. Extremum seeking control for soft landing of an electromechanical valve actuator. Automatica 40 (2004) 1063-1069
17. Popović, D., Janković, M., Manger, S., & Teel, A.R. (2003). Extremum seeking methods for optimization of variable cam timing engine operation. In Proceedings of the American control conference, Denver, Colorado, USA.
18. Sanders J.A., and Verhulst F. Averaging methods in nonlinear dynamical systems (1985), Springer, New York
19. Sontag E. Comments on integral variants of ISS. Systems & Control Letters 34 (1998) 93-100
20. Sontag, E. (2005). Input to state stability: Basic concepts and results. Springer lecture notes in mathematics (CIME Course, Cetraro, June 2004). Berlin: Springer.
21. Sontag E., and Wang Y. Notions of input to output stability. Systems & Control Letters 38 (1999) 235-248
22. Tan, Y., Nešić, D., & Mareels, I. M. Y. (2005). On non-local stability properties of extremum seeking control. In Proceedings of 16th IFAC world congress, Prague, Czech Republic.
23. Teel A.R., Moreau L., and Nešić D. A unified framework for input-to-state stability in systems with two time scales. IEEE Transactions on Automatic Control 48 (2003) 1526-1544
24. Teel A.R., and Nešić D. Averaging with disturbances and closeness of solution. Systems and Control Letters 40 (2000) 317-323
25. Teel A.R., Peuteman J., and Aeyels D. Semi-global practical asymptotic stability & averaging. Systems and Control Letters 37 (1999) 329-334
26. Teel, A. R., & Popović, D. I. (2001). Solving smooth & nonsmooth extremum seeking problems by methods of nonlinear programming. In Proceedings of the American control conference, Washington, DC.
27. Wang H.-H., and Krstić M. Extremum seeking for limit cycle minimization. IEEE Transactions on Automatic Control 45 (2000) 2432-2437
28. Wang H.-H., Yeung S., and Krstić M. Experimental application of extremum seeking on an axial-flow compressor. IEEE Transactions on Control Systems Technology 8 (2000) 300-309