Numerical Problems in Identification of Large Scale Systems

The problem of identifying a SISO discrete linear time invariant system of known order n, where n is large, and with a finite input/output data record, is considered in this paper. It is shown that for the class of least squares identification techniques, there is a fundamental difficulty in carring out such an identification. In particular, it is shown that generically the condition number associated with the parameter estimation problem monotonically increases as the order n increases, and depends on the controllability and observability measures of the system. Moreover, it is shown that some classes of "large scale problems" are intrinsically difficult to correctly identify. An example of a class of large flexible space structures problems is given to show the type of difficulties which may arise for large systems.