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Persistent identification of unstable LTV systems

This paper deals with identification of linear time-varying (possibly unstable and infinite dimensional) systems, perceived as a part of an adaptive system. The main challenges of the problem stem from the following observations: 1) to model the behavior of a time-varying system at a frozen-time moment, only a small window of input/output observations near that time can be used; 2) the signal to the plant is generated by the feedback loop and cannot be manipulated directly, only the external input can be selected at will; and 3) identification of unstable systems mandates closed-loop operation and requires certain model structures, such as ARMAX. This paper addresses issues towards closed-loop identification problems. The problems are first formulated for LTI systems. Essential features of periodic probing signals, including feedback invariance and probing capability, are established which demonstrate their potential utility in closed-loop persistent identification. Error bounds are then established for systems with unstructured unmodeled dynamics and slowly time-varying systems.