Identifiability issues in general interconnected systems

We investigate the problem of identifiability in general interconnected systems. We begin with an arbitrary, structured interconnection of two types of blocks: static nonlinear maps and linear time invariant systems. Indeed, any nonlinear time-invariant dynamical system may be represented as such an interconnection. The blocks may be completely specified or may be unknown and require identification. The input-output dimensions of the unknown blocks are fixed. No other a priori information about them is available. In particular, the static nonlinear maps requiring identification are not naturally parameterized via basis functions or other expansions. The state dimensions of the LTI blocks that require identification are unavailable. Thus, we are interested in non-parametric identification problems. The particular focus of the paper is the issue of “identifiability”. Loosely speaking, a general structured interconnection is identifiable if it is possible to determine the unknown blocks uniquely using input-output experiments alone. As is well known, identifiability concepts are of fundamental importance in system identification. We begin an investigation of identifiability in this context. We offer a characterization of identifiability under certain restrictive assumptions. The computational aspects of this characterization remain to be explored