Optimal adaptive control - Contradiction in terms or a matter of choosing the right cost functional?

IEEE Transactions on Automatic Control

Volumn 53, Issue 8, 2008, Pages 1942-1947

  Krstic, Miroslav ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Adaptive control; Backstepping; Boundary control; Disributed parameter systems

Indexed keywords

AIRCRAFT ENGINES; CONTROL THEORY; DIFFERENTIAL EQUATIONS; INTERSECTIONS; LAWS AND LEGISLATION; LINEAR EQUATIONS; LITHIUM; LYAPUNOV FUNCTIONS; METAL ANALYSIS; NONLINEAR SYSTEMS; PARAMETER ESTIMATION; PARTIAL DIFFERENTIAL EQUATIONS; PROBABILITY DENSITY FUNCTION; QUADRATIC PROGRAMMING; RICCATI EQUATIONS; TELECOMMUNICATION NETWORKS; TRANSIENTS;

ADAPTIVE; ADAPTIVE CONTROL; ADAPTIVE CONTROLS; ADAPTIVE TRACKING CONTROLLERS; BACKSTEPPING; BOUNDARY CONTROL; BOUNDARY CONTROLS; CERTAINTY EQUIVALENCES; COST FUNCTIONAL; DISRIBUTED PARAMETER SYSTEMS; LINEAR QUADRATIC OPTIMAL CONTROLS; LYAPUNOV; NONLINEAR; OPTIMAL CONTROLS; OPTIMAL DESIGNS; OPTIMALITY; PARABOLIC PDE; PARAMETER CONVERGENCES; PARAMETER ERRORS; PARAMETER ESTIMATION ERRORS; POSITIVE DEFINITE; QUADRATIC COSTS; TECHNICAL IDEAS; TIME-STEP; VALUE FUNCTIONS;

ADAPTIVE CONTROL SYSTEMS;

EID: 54049145831     PISSN: 00189286     EISSN: None     Source Type: Journal    
DOI: 10.1109/TAC.2008.929464     Document Type: Article

References (23)

1. J. Bentsman and Y. Orlov, "Reduced spatial order model reference adaptive control of spatially varying distributed parameter systems of parabolic and hyperbolic types," Int. J. Adapt. Control Signal Process., vol. 15, pp. 679-696, 2001.
2. M. Bohm, M. A. Demetriou, S. Reich, and I. G. Rosen, "Model reference adaptive control of distributed parameter systems," SIAM J. Control Optim., vol. 36, no. 1, pp. 33-81, 1998.
3. M. S. de Queiroz, D. M. Dawson, M. Agarwal, and F. Zhang, "Adaptive nonlinear boundary control of a flexible link robot arm," IEEE Trans. Robotics Autom., vol. 15, no. 4, pp. 779-787, Aug. 1999.
4. T. E. Duncan, B. Maslowski, and B. Pasik-Duncan, "Adaptive boundary and point control of linear stochastic distributed parameter systems," SIAM J. Control Optim., vol. 32, no. 3, pp. 648-672, 1994.
5. G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, 2nd ed. Cambridge, U.K.: Cambridge University Press, 1959.
6. K. S. Hong and J. Bentsman, "Direct adaptive control of parabolic systems: Algorithm synthesis, and convergence, and stability analysis," IEEE Trans. Autom. Control, vol. 39, no. 10, pp. 2018-2033, Oct. 1994.
7. P. Ioannou and J. Sun, Robust Adaptive Control. Englewood Cliffs, NJ: Prentice-Hall, 1996.
8. M. Jovanovic and B. Bamieh, "Lyapunov-based distributed control of systems on lattices," IEEE Trans. Autom. Control, vol. 50, no. 4, pp. 422-433, Apr. 2005.
9. T. Kobayashi, "Adaptive regulator design of a viscous Burgers' system by boundary control," IMA J. Mathemat. Control and Infom., vol. 18, pp. 427-437, 2001.
10. T. Kobayashi, "Adaptive stabilization of the Kuramoto-Sivashinsky equation," Int. J. Syst. Sci., vol. 33, pp. 175-180, 2002.
11. M. Krstic, I. Kanellakopoulos, and P. Kokotovic, Nonlinear and Adaptive Control Design. New York: Wiley, 1995.
12. M. Krstic and A. Smyshlyaev, "Adaptive boundary control for unstable parabolic PDEs - Part I: Lyapunov design," IEEE Trans. Autom. Control, vol. 53, no. 7, Aug. 2008.
13. Z. H. Li and M. Krstic, "Optimal design of adaptive tracking controllers for nonlinear systems," Automatica, vol. 33, pp. 1459-1473, 1997.
14. W. Liu and M. Krstic, "Adaptive control of Burgers' equation with unknown viscosity," Int. J. Adaptive Control and Signal Process., vol. 15, pp. 745-766, 2001.
15. H. Logemann and B. Martensson, "Adaptive stabilization of infinite-dimensional systems," IEEE Trans. Autom. Control, vol. 37, no. 12, pp. 1869-1883, Dec. 1992.
16. P. J. Moylan and B. D. O. Anderson, "Nonlinear regulator theory and an inverse optimal control problem," IEEE Trans. Autom. Control, vol. AC-18, pp. 460-465, 1973.
17. Y. Orlov, "Sliding mode observer-based synthesis of state derivative-free model reference adaptive control of distributed parameter systems," J. Dynam. Syst., Meas., and Control, vol. 122, pp. 726-731, 2000.
18. R. Sepulchre, M. Jankovic, and P. Kokotovic, Constructive Nonlinear Control. New York: Springer, 1997.
19. A. Smyshlyaev and M. Krstic, "Closed form boundary state feedbacks for a class of 1-D partial integro-differential equations," IEEE Trans. Autom. Control, vol. 49, no. 12, pp. 2185-2202, Dec. 2004.
20. A. Smyshlyaev and M. Krstic, "Adaptive boundary control for unstable parabolic PDEs - Part II: Estimation-based designs," Automatica, vol. 43, pp. 1543-1556, 2007.
21. A. Smyshlyaev and M. Krstic, "Adaptive boundary control for unstable parabolic PDEs - Part III: Output-feedback examples with swapping identifiers," Automatica, vol. 43, pp. 1557-1564, 2007.
22. S. Townley, "Simple adaptive stabilization of output feedback stabilizable distributed parameter systems," Dynam. Control, vol. 5, pp. 107-123, 1995.
23. J. T.-Y. Wen and M. J. Balas, "Robust adaptive control in Hilbert space," J. Mathemat. Anal. Applic., vol. 143, pp. 1-26, 1989.