Abstract
The problem of constructing a model reference adaptive control law for an uncertain 1-dimensional parabolic system is considered in this article. The controller designed here involves only the plant state but no its derivatives. A priori bounds on the plant’s uncertain parameters are used to propose switching laws which serve as an adaptive mechanism. The exponential decay to zero of the state error with any prescribed rate is guaranteed by choosing a controller parameter correspondingly. Numerical studies are also presented to illustrate the applicability of the control law.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Liu W, Elementary Feedback Stabilization of the Linear Reaction-Convection-Diffusion Equation and the Wave Equation, Springer-Verlag, Berlin Heidelberg, 2010.
Chentouf B and Wang J M, Stabilization of a one-dimensional dam-river system: A nondissipative and noncollocated case, Journal of Optimization Theory and Applications, 2007, 134(2): 223–239.
Chentouf B and Wang J M, A Riesz basis methodology for proportional and integral output regulation of a one-dimensional diffusive wave equation, SIAM Journal on Control and Optimization, 2008, 47(5): 2275–2302.
Hong K S and Bentsman J, Application of averaging method for integro-differential equations to model reference adaptive control of parabolic system, Automatica, 1994, 30(9): 1415–1419.
Hong K S and Bentsman J, Direct adaptive control of parabolic systems: Algorithm synthesis and convergence and stability analysis, IEEE Transactions on Automatic Control, 1994, 39(10): 2018–2033.
Böhm M, Demetriou A A, Reich S, and Rosen I G, Model reference adaptive control of distributed parameter systems, SIAM J. Control Optim., 1998, 36(1): 33–81.
Bentsman J and Orlov Y, Reduced spatial order model reference adaptive control of spatially varying distributed parameter systems of parabolic and hyperbolic types, Int. J. Adapt. Control Signal Process, 2001, 15: 679–696.
Demetriou M A and Rosen I G, Variable structure model reference adaptive control of parabolic distributed parameter systems, Proc. the American Control Conf., May 2002, 4371–4376.
Hsu L, de Araujo A D, and Costa R R, Analysis and design of I/O based variable structure adaptive control, IEEE Transactions on Automatic Control, 1994, 39: 4–21.
Evans L C, Partial Differential Equations, Graduate Studies in Mathematics, Vol. 19, American Mathematical Society, 1998.
Temam R, Infinite-Dimensional Dynamical Systems in Mechanics and Physics, Applied Mathematical Science, Vol. 68, Springer-Verlag, New York, 1988.
Trefethen L N, Spectral Methods in Matlab, SIAM, Philadelphia, PA, 2000.
Author information
Authors and Affiliations
Corresponding author
Additional information
This paper was partially supported by State Scholarship Fund of China under Grant No. 2010602510 from China Scholarship Council (CSC), the National Natural Science Foundation of China under Grant No. 11101082, the Program for Innovative Research Team in UIBE, the research foundation of University of International Business and Economics under Grant No. 7500010336, and the National Natural Science Foundation of China under Grant Nos. 10626002, 61374088 and 71371024.
This paper was recommended for publication by Editor ZHANG Jifeng.
Rights and permissions
About this article
Cite this article
Jia, C., Shao, ZC. State derivative-free variable structure model reference adaptive control of linear parabolic systems. J Syst Sci Complex 26, 957–967 (2013). https://doi.org/10.1007/s11424-013-2154-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11424-013-2154-x