Kernels of anticausal operators and the multivariable generalised predictive control problem

Eigenvector or principal direction projections provide a convenient means of decomposing the multivariable problem into a set of scalar control problems, each of which can be solved using single-input single-output generalised predictive control. However the bicausal nature of eigenvector or principal direction representations leads to anticausality difficulties which in the past have been overcome by a `forward´ shift in the control horizon. Under some circumstances this shift introduces an undesirable pseudo-delay, and a previous paper proposed the use of `kernels´ of bicausal operators as an effective remedy for the scalar case. In the paper the authors explore the relationship between these kernels and scaling of the bicausal representations and propose algorithms which overcome the pseudo-delay problems in the multivariable case