@inproceedings{bb5514c560224a3d90d5e12478a71057,
title = "Sliding mode boundary control of unstable parabolic pde systems with parameter variationsand matched disturbances",
abstract = "This paper considers the stabilization problem of a one-dimensional unstable heat conduction system subject toparametric variations and boundary uncertainties. This system is modeled as a parabolic partial differential equation (PDE) and is only powered from one boundary with a Dirichlet type of actuator. By taking the Volterra integral transformation, we obtain a nominal PDE with asymptotic stability characteristics in the new coordinates when an appropriate boundary control input is applied. The associated Lyapunov function can then be used for designing an infinite-dimensional sliding surface, on which the system exhibits exponential stability, invariant of the bounded matched disturbance, and is robust against certain types of parameter variations. A continuous variable structure boundary control law is employed to attain the sliding mode on the sliding surface. The proposed method can be extended to other parabolic PDE systems such as diffusion-advection system. Simulation results are demonstrated and compared with the other outstanding back-stepping control schemes.",
keywords = "Boundary control, Chattering, Distributedparameter systems, Lyapunov methods, Sliding surface",
author = "Cheng, \{Meng Bi\} and Verica Radisavljevic and Su, \{Wu Chung\}",
year = "2009",
doi = "10.1109/ACC.2009.5160481",
language = "English",
isbn = "9781424445240",
series = "Proceedings of the American Control Conference",
pages = "4085--4095",
booktitle = "2009 American Control Conference, ACC 2009",
note = "2009 American Control Conference, ACC 2009 ; Conference date: 10-06-2009 Through 12-06-2009",
}