Identification of Probabilistic System Uncertainty Regions by Explicit Evaluation of Bias and Variance Errors

A procedure is developed for identification of probabilistic system uncertainty regions for a linear time-invariant system with unknown dynamics, on the basis of time sequences of input and output data. The classical framework is handled in which the system output is contaminated by a realization of a stationary stochastic process. Given minor and verifiable prior information on the system and the noise process, frequency response, pulse response, and step response confidence regions are constructed by explicitly evaluating the bias and variance errors of a linear regression estimate. In the model parameterizations, use is made of general forms of basis functions. Conservatism of the uncertainty regions is limited by focusing on direct computational solutions rather than on closed-form expressions. Using an instrumental variable method for identification, the procedure is suitable also for input–output data obtained from closed-loop experiments.