Adaptive control of PDES
Periodic Control Systems, Volume # 3 | Part# 1
Miroslav Krstic; Andrey Smyshlyaev
Digital Object Identifier (DOI)
backstepping,distributed parameter systems,adaptive control
This paper presents several recently developed techniques for adaptive control of PDE systems. Three different design methods are employed--the Lyapunov design, the passivity-based design, and the swapping design. The basic ideas for each design are introduced through benchmark plants with constant unknown coefficients. It is then shown how to extend the designs to reactionadvection-diffusion PDEs in 2D. Finally, the PDEs with unknown spatially varying coefficients and with boundary sensing are considered, making the adaptive designs applicable to PDE systems with an infinite relative degree, infinitely many unknown parameters, and open loop unstable.
 Bentsman, J. and Y. Orlov (2001). Reduced spatial order model reference adaptive control of spatially varying distributed parameter systems of parabolic and hyperbolic types. Int. J. Adapt. Control Signal Process. 15, 679- 696.  Bohm, M., M. A. Demetriou, S. Reich and I. G. Rosen (1998). Model reference adaptive control of distributed parameter systems. SIAM J. Control Optim. 36(1), 33-81.  Hong, K. S. and J. Bentsman (1994). Direct adaptive control of parabolic systems: Algorithm synthesis, and convergence, and stability analysis. IEEE Trans. Automatic Control 39, 2018-2033.  Ioannou, P. and J. Sun (1996). Robust Adaptive Control. Prentice Hall.  Krstic, M. (2005). Lyapunov adaptive stabilization of parabolic pdes--part i: A benchmark for boundary control. In: CDC-ECC.  Krstic, M., I. Kanellakopoulos and P. Kokotovic (1995). Nonlinear and Adaptive Control Design . Wiley, New York.  Liu, W. and M. Krstic (2001). Adaptive control of Burgers' equation with unknown viscosity. Int. J. Adaptive Control and Signal Processing 15, 745-766.  Praly, L. (1992). Adaptive regulation: Lyapunov design with a growth condition. International Journal of Adaptive Control and Signal Processing 6, 329-351.  Smyshlyaev, A. and M. Krstic (2004). Closed form boundary state feedbacks for a class of 1D partial integro-differential equations. IEEE Trans. Auto. Contr. 49, 2185-2202.  Smyshlyaev, A. and M. Krstic (2006a). Adaptive boundary control of reaction-diffusion-advection PDEs with spatially varying parameters. In: American Control Conference.  Smyshlyaev, A. and M. Krstic (2006b). Output-feedback adaptive control for parabolic PDEs with spatially varying coefficients. In: IEEE Conference on Decision and Control.  Smyshlyaev, A. and M. Krstic (2007a). Adaptive boundary control for unstable parabolic PDEs--Part II: Estimation-based designs. Automatica.  Smyshlyaev, A. and M. Krstic (2007b). Adaptive boundary control for unstable parabolic PDEs--Part III: Output-feedback examples with swapping identifiers. Automatica..