The average-case identifiability and controllability of large scale systems

Needs for increased product quality, reduced pollution, and reduced energy and material consumption are driving enhanced process integration. This increases the number of manipulated and measured variables required by the control system to achieve its objectives. This paper addresses the question of whether processes tend to become increasingly more difficult to identify and control as the process dimension increases. Tools and results of multivariable statistics are used to show that, under a variety of assumed distributions on the elements, square processes of higher dimension tend to be more difficult to identify and control, whereas the expected controllability and identifiability of nonsquare processes depends on the relative numbers of measured and manipulated variables. These results suggest that the procedure of simplifying the control problem so that only a square process is considered is a poor practice for large scale systems.