CLF-based control design for unknown multiinput bonlinear systems with good transient performance

IEEE Transactions on Automatic Control

Volumn 55, Issue 11, 2010, Pages 2635-2640

  Kosmatopoulos, Elias B ^a,b  

^a DEMOCRITUS UNIVERSITY OF THRACE   (Greece)

^b INFORMATION TECHNOLOGIES INSTITUTE   (Greece)

Author keywords

Control Lyapunov functions (CLFs); multivariable adaptive control; semidefinite programming; sum of squares (SOS)

Indexed keywords

ADAPTIVE CONTROL; CLOSED-LOOP PERFORMANCE; CLOSED-LOOP TRANSIENT PERFORMANCE; CONTROL DESIGN; CONTROL LYAPUNOV FUNCTION; CONTROL SCHEMES; CONTROLLED SYSTEM; MATHEMATICAL ANALYSIS; MULTIINPUT; MULTIVARIABLE ADAPTIVE CONTROL; SEMIDEFINITE PROGRAMMING; SUM OF SQUARES; TECHNICAL NOTES; TRANSIENT PERFORMANCE;

ADAPTIVE CONTROL SYSTEMS; CONTROL THEORY; COUPLINGS; DIFFERENTIAL EQUATIONS; FEEDBACK; LYAPUNOV FUNCTIONS; LYAPUNOV METHODS; NONLINEAR FEEDBACK; STATE FEEDBACK; SYSTEMS ENGINEERING;

MATHEMATICAL PROGRAMMING;

EID: 78149232227     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2010.2063190     Document Type: Article

References (22)

1. C. Berg, J. P. R. Christensen, and P. Ressel, "Positive definite functions on abelian semigroups," Math. Annu., vol. 223, pp. 253-274, 1976.
2. S. Burer, R. D. C. Monteiro, and Y. Zhang, "A computational study of a gradient-based log-barrier algorithm for a class of large-scale SDPs," Math. Programming, Series B, vol. 95, no. 2, pp. 359-379, 2003.
3. J. W. Curtis and R. W. Beard, "Satisficing: A new approach to constructive nonlinear control," IEEE Trans. Autom. Control, vol. 49, no. 7, pp. 1090-1102, Jul. 2004.
4. P. A. Ioannou and J. Sun, Stable and Robust Adaptive Control. En- glewood Cliffs, NJ: Prentice-Hall, 1995.
5. H. K. Khalil, Nonlinear Systems. New York: Macmillan, 1992.
6. E. B. Kosmatopoulos and P. A. Ioannou, "Robust switching adaptive control of multiinput nonlinear systems," IEEE Trans. Autom. Control, vol. 47, no. 4, pp. 610-624, Apr. 2002.
7. E. B. Kosmatopoulos, "Adaptive control design based on adaptive optimization principles," IEEE Trans. Autom. Control, vol. 53, no. 11, pp. 2680-2685, Dec. 2008.
8. M. Krstic, I. Kanellakopoulos, and P. V. Kokotovic, Nonlinear and Adaptive Control Design. New York: Wiley, 1995.
9. J. B. Lasserre, "A sum of squares approximation of nonnegative polynomials," SIAMRev., vol. 49, no. 4, pp. 651-669, 2007.
10. d) by neural networks and mixture networks," IEEE Trans. Neural Netw., vol. 9, no. 5, pp. 969-978, Sep. 1998.
11. S. P. Moustakidis, G. A. Rovithakis, and J. B. Theocharis, "An adaptive neuro-fuzzy tracking control for multiinput nonlinear dynamic systems," Automatica, vol. 44, no. 5, pp. 1418-1425, 2008.
12. P. A. Parrilo, "Structured Semidefinite Programs and Semialgebraic Geometry Methods in Robustness and Optimization," Ph.D. dissertation, California Inst. Technol., Pasadena, CA, 2000.
13. P. A. Parrilo, S. Prajna, A. Papachristodoulou, and P. Seiler, SOSTOOLS Software Tech. Rep., 2010 [Online]. Available: http://www.cds.caltech.edu/ sostools/
14. M. M. Peet and P.-A. Bliman, "Polynomial lyapunov functions for exponential stability of nonlinear systems on bounded regions," in Proc. IFAC World Congr., Seoul, Korea, Jun. 6-11, 2008, [CD ROM].
15. J.-B. Pomet, "Remarks on sufficient information for adaptive nonlinear regulation," in Proc. 31st IEEE Conf. Decision Control, Tucson, AZ, 1992, pp. 1737-1741.
16. S. Prajna, A. Papachristodoulou, and F. Wu, "Nonlinear control synthesis by sum of squares optimization: A Lyapunov-based approach," in Proc. Asian Control Conf., 2004, pp. 157-165.
17. S. S. Sastry and A. Isidori, "Adaptive control of linearizable systems," IEEE Trans. Autom. Control, vol. 34, no. 11, pp. 405-412, Nov. 1989.
18. E. D. Sontag, "A universal construction of arstein's theorem on nonlinear stabilization," Syst. Control Lett., vol. 13, pp. 117-123, 1989.
19. NI. Sznaier, J. Cloutier, R. Hull, D. Jacques, and C. Mracekt, "A receding horizon state dependent Riccati equation approach to suboptimal regulation of nonlinear systems," in Proc. 37th IEEE Conf. Decision Control, Tampa, FL, Dec. 1998, pp. 1792-1797.
20. J. Tsinias, "Sufficient Lyapunov-like conditions for stabilization," Math. Control Sign., Syst., vol. 2, pp. 343-357, 1989.
21. S. R. Weller and G. C. Goodwin, "Hysteresis switching adaptive control of linear multivariable systems," IEEE Trans. Autom. Control, vol. 39, no. 7, pp. 1360-1375, Jul. 1994.
22. T. P. Zhang and S. S. Ge, "Adaptive neural control of MIMO nonlinear state time-varying delay systems with unknown dead-zones and gain signs," Automatica, vol. 43, pp. 1021-1033, 2007.