Persistent identification of time-varying systems

Identification of time-varying systems, especially slowly time-varying systems, is of importance in the development of a comprehensive theory of adaptation. The persistent identification measures employed in this paper capture a main characterization in such identification problems, namely, one input signal must be used for identification of all possible observation windows. This paper establishes several essential features in persistent identification problems which highlight their potential utility in adaptation: 1) they have computable upper and lower bounds for typical classes of prior uncertainty sets; 2) any full rank n-periodic signals are optimal, and the simple least-squares estimates are optimal identification algorithms; 3) optimal probing inputs can be approximately generated in a closed-loop configuration when the plant and the controller are slowly time-varying; and 4) n-periodic signals are asymptotically optimal for slowly time-varying systems. The main results of this paper have been successfully combined with a certain slow H^∞ design to derive an adaptive stabilization scheme