Generalization of Feedback Error Learning to MIMO Systems and its Stability Proof

Basel A. Al-Ali (0451127)



Learning control is a promising control method since it provides a good performance by on-line learning, without a mathematical model of the object to be controlled. Recently, a new learning control scheme named feedback error learning (FEL) has been proposed and attracted much attention. A striking feature of this scheme is that it uses a feedforward controller which is adjusted by some learning law. This thesis generalizes the FEL scheme to multi-input multi-output (MIMO) systems and then proves the stability of the generalized scheme. The concept of interactor matrix plays a key role to treat MIMO systems not necessarily biproper.

Firstly, the existence of an ideal inverse of the system is shown by means of the interactor. Since the system is not necessarily invertible with properness, the inverse is attained by a feedforward controller with compensation by a pre-filter. Secondly, the learning law for the feedforward controller is given so that the parameter tends to the ideal value. Thirdly, the thesis gives two kinds of stability proof in order to guarantee convergence of the parameter. Numerical simulation for various examples has been performed to show the effectiveness of the scheme.