2-D analysis based iterative learning control for linear discrete-time systems with time delay
Iterative Learning Control (ILC) technique, based on the theory of two-dimensional (2-D) systems, is well developed for linear continuous time-delay systems and linear discrete-time systems. Grounded on the 2-D linear continuous-discrete Roesser's model, the ILC process is investigated in the paper for linear discrete-time systems with constant time delay \[ x(t+1) = Ax(t)+A_1x(t-\tau)+Bu(t), \qquad y(t)=Cx(t)+Du(t), \] where \(t \in T_0 = \{0, 1, \dots , T\}\), \(x(t) \in\mathbb R^n\) is the state vector, \(u(t) \in\mathbb R^m\) is the input vector, and \(y(t) \in\mathbb R^p\) is the output vector. A sufficient condition is obtained providing that the system output \(y(t,k)\) converges asymptotically to the reference trajectory \(y_r(t)\) under the proposed ILC rule \(u(t, k+1)= u(t, k) + K e(t, k)\), i.e., \(e(t, k)= y_r(t) - y(t,k) \to 0\) when \(k \to \infty\). Numerical results are presented to illustrate the proposed scheme.
scientific article; zbMATH DE number 5906859