Model-Based Processing

6Deterministic Subspace Identification

6.1 Introduction

The basic problem in this text is to identify a state‐space model, linear or nonlinear, from data. Subspace IDentification (SID) is a technique to extract a black‐box model in generic state‐space form from uncertain input/output data using robust, numerically stable, linear algebraic methods. SID performs a black‐box identification of a linear, time‐invariant, state‐space model from uncertain measurements. Recall that a subspace is a space or subset of a parent space that inherits some or all of its characteristics. Unlike the MBID discussed in the previous chapter, it does not require any specific structure of the state‐space model only its order (number of states) that can be derived directly from the embedded linear algebraic decomposition. In this chapter, subspace refers primarily to a vector (state) space in which its essential characteristics can be captured by a “smaller” space – the subspace. For example, an th order state‐space dynamic system can be approximated by an th order () system capturing the majority of its properties. ...