Optimal Iterative Learning Control for square MIMO linear systems

In this paper, a modified learning gain for Iterative Learning Control (ILC) approach is proposed for linear Multi-Input-Multi-Output repetitive systems. The control law synthesis is based on the resolution of a quadratic criterion which minimizes the error between the setpoint references and the system outputs at each iteration for each trial. The resolution of the control problem leads to a new gain which avoids matricial inversion problems appeared with classical ILC algorithms such as direct model inversion (I-ILC) and optimal ILC (Q-ILC). The modified type ILC approach improves the learning convergence significantly compared to I-ILC and Q-ILC algorithms. Furthermore, a sufficient and necessary stability condition and convergence properties are established. Simulations with a MIMO Mass-spring damper system show the effectiveness of the proposed method.