Towards Finite Sample Networked System Identification: A Cascade Network Example

Abstract

Finite sample system identification (FSID) methods construct confidence regions for system parameters with non-asymptotic guarantees under minimal assumptions on the noise distribution. This paper deals with constructing non-asymptotic confidence region using Sign Perturbed Sums (SPS) approach for a linear module in a cascade of dynamical systems. In dynamic networks every measurement is usually contaminated with noise. However, the SPS approach was originally devised for systems with no noise on the input. The SPS approach was extended to Errors-In-Variables (EIV) systems where both the input and the output signal are measured in noise under the assumption that the true input signal is an independent sequence. However, in a dynamic network the input of a module is not usually an independent sequence since it is typically the output of another dynamical system. In this paper the SPS approach is extended to EIV systems without making any assumption on the true input signal. Then, the approach is used to construct confidence region for a single module in a simple cascade network by incorporating additional data and taking advantage of the cascade structure. This is done without estimating other modules in the network. The method is illustrated in numerical experiments.