Finite-diimensional compensator for a class of uncertain distributed parameter systems

Abstract

In the development of feedback control for distributed parameter systems (DPSs), i.e. systems described by partial differential equations, it is important to maintain ihe finite dimensionality of the controller even though the DPS is infinite-dimensional. In previous work, scientists proposed some available design method of the finite-dimensional feedback control for certain DPSs. Unfortunately, in real engineering systems, the external disturbances or/and modelling errors almost always exist and some other new control design must be presented. In this paper a novel finite-dimensional, robust control is proposed for a class of uncertain distributed parameter systems. The ultimate boundedness of the closed-loop with the controls designed here can be ensured and the bounds can be arbitrarily small, provided that the dimension of the dynamical compensator is large enough and the boundary layer is sufficiently small, even though the observation spillover appears.