Networked and Delayed Recursive Identification of Nonlinear Systems

The paper presents a new recursive prediction error algorithm for joint identification of a time invariant nonlinear state space model and a delay. The parametrization of the state space model is polynomial. The delay parameter is embedded in the output equation of the continuous time model. This allows the gradient to be computed directly by differentiation, which leads to a recursive algorithm that exploits an integrated recursive correlation for identification of the delay. Multiple dynamic models and gradients, for a selected range of integer delays, are applied for delay discretization. Interpolation between the integer delay models then enables identification of the fractional part of the delay. The algorithm is shown to provide highly accurate results in a numerical example when processing a relatively small data set. The general motivation for the work is the emerging wireless 5G standards, whose latencies are specified to enable new networked feedback control and virtual reality based applications using so called critical machine type communication. To support this development there is a need for nonlinear system identification methods that are able to compensate for the often still significant network delays.