On-Line Identification of Unstable Processes Subject to Unbounded Disturbances

An on-line scheme for identifying stable or unstable linear time-invariant processes subject to a class of deterministic and/or stochastic disturbances is proposed. The disturbances are restricted to be the outputs of some unknown linear time-invariant system. The identification scheme consists of 1) a probing signal input which is a sum of sinusoids (exponentially increasing sum of sinusoids when the process is unstable or the disturbances are unbounded), 2) linear time -varying filters which have the properties of asymptotic stability, asymptotic signal tracking and asymptotic noise anhilation and 3) a parameter update algorithm which uses the filtered input, output data. The frequency response of the process (at the probing signal frequencies) are also estimated. The proposed scheme is verified by simulation.