On Iterative Learning Control of Parabolic Distributed Parameter Systems
C. Xu, R. Arastoo and E. Schuster
17th Mediterranean Conference on Control and Automation
Thessaloniki, Greece, June 24 - 26, 2009
Abstract
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The Iterative Learning Control (ILC) technique
is extended to distributed parameter systems governed by
parabolic partial differential equations (PDEs). ILC arises
as an effective method to approach constrained optimization
problems in PDE systems. We discuss both P-type and D-type
ILC schemes for a distributed parameter system formulated as
a general linear system (A,B,C,D) on a Hilbert space, in
which the system operator A generates a strongly continuous
semigroup. Under the assumption of identical initialization
condition (IIC), conditions on the learning parameters are
obtained to guarantee convergence of the P-type and D-type
ILC schemes. Numerical simulations are presented for a 1D
heat conduction control problem solved using ILC based on
semigroup analysis. The numerical results show the effectiveness
of the proposed ILC schemes.