On Iterative Learning Control of parabolic distributed parameter systems

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 Sigma(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.