Robust MRAC of a nonautonomous parabolic system with spatiotemporally varying coefficients and bounded disturbance

Asian Journal of Control

Volumn 5, Issue 3, 2003, Pages 350-363

  Yang, Kyung Jinn ^a   Hong, Keum Shik ^a  

^a Pusan National University   (South Korea)

Author keywords

Parabolic partial differential equation; Persistence of excitation; Robust model reference adaptive control; Stability; Uniform ultimate boundedness

Indexed keywords

COMPUTER SIMULATION; MATHEMATICAL MODELS; PARAMETER ESTIMATION; PARTIAL DIFFERENTIAL EQUATIONS; ROBUSTNESS (CONTROL SYSTEMS);

EXCITATION PERSISTENCE; PARABOLIC PARTIAL DIFFERENTIAL EQUATION; PARAMETER ERROR CONVERGENCE; ROBUST MODEL REFERENCE ADAPTIVE CONTROL; UNIFORM ULTIMATE BOUNDEDNESS;

ADAPTIVE CONTROL SYSTEMS;

EID: 1442303324     PISSN: 15618625     EISSN: None     Source Type: Journal    
DOI: 10.1111/j.1934-6093.2003.tb00127.x     Document Type: Article

References (35)

1. Ammari, K., Z. Liu, and M. Tucsnak, Decay Rates for a Beam with Pointwise Force and Moment Feedback, Math. Contr. Signals Syst., Vol.15, pp.229-255 (2002)
2. Balas, M. J., Stable Feedback Control of Linear Distributed Parameter Systems: Time and Frequency Domain Conditions, J. Math. Anal. Appl., Vol.225, pp.114-167 (1998).
3. Banks, H.T. and R. C. Smith, Parameter Estimation in a Structural Acoustic System with Fully Nonlinear Coupling Conditions, Math. Comput. Model., Vol.23, No.4, pp.17-50 (1996).
4. Bentsman, J. and Y. Orlov, Reduced Spatial Order Model Reference Adaptive Control of Spatially Varying Distributed Parameter Systems of Parabolic and Hyperbolic Types, Int. J. Adapt. Contr. Signal Process., Vol.15, pp.679-696 (2001).
5. Bohm, M., M. A. Demetriou, S. Reich, and I. G. Rosen, Model Reference Adaptive Control of Distributed Parameter Systems, SIAM J. Contr. Optim., Vol.36, No.1, pp.33-81(1998).
6. Boue, M. and P. Dupuis, Risk-sensitive and Robust escape Control for Degenerate Diffusion Processes, Math. Contr. Signals Syst., Vol.14, pp.62-85 (2001).
7. Duncan, T. E., B. Maslowski, and B. Pasik-Duncan, Adaptive Boundary and Point Control of Linear Stochastic Distributed Parameter Systems, SIAM J. Contr. Optim., Vol.32, pp.648-672 (1994).
8. Friedman, A., Partial Differential Equations, Holt, Reinhart, and Winston, New York (1969).
9. ∞-control of a Distributed Parameter System with Non-minimum phase, Int. J. Contr., Vol.53, pp.45-79 (1989).
10. Ho, T. T., P. W. Fieguth, and A. S. Willsky, Computationally Efficient Steady-state Multiscale Estimation for 1-D Diffusion Processes, Automatica, Vol.37, pp.325-340 (2001).
11. Hong, K. S., Asymptotic Behavior Analysis of a Coupled Time-varying System: Application to Adaptive Systems, IEEE Trans. Automat. Contr., Vol.42, No.12, pp.1693-1697 (1997).
12. Hong, K. S. and J. Bentsman, Direct Adaptive Control of Parabolic Systems: Algorithm Synthesis, Convergence, and Stability Analysis, IEEE Trans. Automat. Contr., Vol.39, No.10, pp.2018-2033 (1994).
13. Hong, K. S. and J. Bentsman, Application of Averaging Method for Integro-differential Equations to Model Reference Adaptive Control of Parabolic Systems, Automatica, Vol.30, No.9, pp.1415-1419 (1994).
14. Hong, K. S., V. Solo, and J. Bentsman, Adaptive Control of a Time-varying Parabolic System: Averaging Analysis, Proc. 14th World Congr. IFAC, Beijing, China, pp.351-356 (1999).
15. Hong, K. S. and K. J. Yang, Partial Convergence of Coupled Time-varying Systems, Proc. IFAC SYSID 2000, Santa Barbara, California (2000).
16. Logemann, H. and E. P. Ryan, Time-varying and Adaptive Discrete-time Low-gain Control of Infinite-dimensional Linear Systems with Input Nonlinearities, Math. Contr. Signals Syst., Vol.13, pp.293-317(2000).
17. Mitrinovic, D. S., J. E. Pecaric, and A. M. Fink, Inequalities Involving Functions and Their Integrals and Derivatives, Kluwer Academic, Dordrecht (1991).
18. Oostveen, J. C. and R. F. Curtain, Robustly Stabilizing Controllers for Dissipative Infinite-dimensional Systems with Collocated Actuators and Sensors, Automatica, Vol.36, No.3, pp.337-348 (2000).
19. Orlov, Y. and J. Bentsman, Adaptive Distributed Parameter Systems Identification with Enforceable Identifiability Conditions and Reduced-order Spatial Differentiation, IEEE Trans. Automat. Contr., Vol.45, No.2, pp.203-216 (2000).
20. Padhi, R., S. N. Balakrishnan, and T. Randolph, Adaptive-critic Based Optimal Neuro Control Synthesis for Distributed Parameter Systems, Automatica, Vol.37, pp.1223-1234 (2001).
21. Pasik-Duncan, B. Identification and Adaptive Control of Some Stochastic Distributed Parameter Systems, Int. J. Adapt. Contr. Signal Process., Vol.15, pp.565-587 (2001).
22. Pazy, A., Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York (1983).
23. Rebarber, R. and S. Townley, Robustness with Respect to Delays for Exponential Stability of Distributed Parameter Systems, SIAM J. Contr. Optim., Vol.37, pp.230-244 (1998).
24. Reinschke, J., M. W. Cantoni, and M. C. Smith, A robust Control Framework for Linear, Time-invariant, Spatially Distributed Systems, SIAM J. Contr. Optim., Vol.40, pp.610-627 (2001).
25. Renou, S., M. Perrier, D. Dochain, and S. Gendron, Direct Adaptive Control of a Linear Parabolic System, Proc. IFAC SYSID 2000, Santa Barbara, California (2000).
26. ∞-control of Diffusion Systems by Using a Finite-dimensional Controller, SIAM J. Contr. Optim., Vol.37, pp.409-428 (1998).
27. Showalter, R. E., Hibert Space Methods for Partial Differential Equations, Pitman Advanced Publishing Program, San Francisco (1977).
28. Walker, J. A., Dynamical Systems and Evolution Equations, Plenum Press, New York (1980).
29. Wen, J. and M. Balas, Robust Adaptive Control in Filbert Space, J. Math Anal. Appl., Vol.143, pp.1-26 (1989).
30. Winkin, J. J., D. Dochain, and P. Ligarius, Dynamical Analysis of Distributed Parameter Tubular Reactors, Automatica, Vol.36, pp.349-361 (2000).
31. Xiao, M. and T. Basar, Center Manifold of the Viscous Moore-Greitzer PDE Model, SIAM J. Appl. Math., Vol.61, No.3, pp.855-869 (2001).
32. Yang, K. J., K. S. Hong, E. J. Rhee, and W. S. Woo, Model Reference Adaptive Control of a Flexible Structure, KSME Int. J., Vol.15, No.10, pp.1356-1368 (2001).
33. Yang, K. J., K. S. Hong, W. S. Yoo, and O. K. Lim, Robust Adaptive Control of a Time-varying Heat Equation with Unknown Bounded Disturbance, JSME Int. J., Ser. C, Vol.44, No.3, pp.708-716 (2001).
34. Yang, K. J., K. S. Hong, W. S. Yoo, and F. Matsuno, Model Reference Adaptive Control of a Cantilevered Flexible Beam, JSME Int. J., Ser. C, Vol.46, No.2, pp.1-12 (2003).
35. Yu, W., Identification for Parabolic Distributed Parameter Systems with Constraints on the Parameters and the State, SIAM J. Contr. Optim., Vol.33, pp.1801-1815 (1995).