OPTIMALLY ROBUST SYSTEM-IDENTIFICATION OF SYSTEMS SUBJECT TO AMPLITUDE-BOUNDED STOCHASTIC DISTURBANCES

In this contribution it is shown that log cos (pi x/(2C)) is the optim ally robust criterion function for prediction error methods with respe ct to amplitude-bounded stochastic disturbances. This criterion functi on minimizes the maximum asymptotic covariance matrix of the parameter estimates for the family of innovations of the system which are ampli tude bounded by the constant C. Furthermore, the stochastic worst case performance of the estimate corresponding to the criterion function l og cos (pi x/(2C)) is better than the worst case performance of the le ast squares estimate even if the constant C is chosen larger than the actual amplitude bound on the innovations. In addition to its favorabl e properties in a stochastic setting, this criterion function also gen erates estimates which are unfalsified in a deterministic framework.