PERSISTENT IDENTIFICATION OF TIME-VARYING SYSTEMS

In this paper, the problem of identification of time-varying systems i s investigated in the framework of worst-case identification and infor mation-based complexity, Measures of intrinsic errors, termed persiste nt identification errors, in such identification problems are introduc ed, For a selected model space of dimension n (finite impulse response models) and an observation window of length m, the persistent identif ication measures provide the worst case posterior identification error s over all possible starting times of the observation windows when the input and identification algorithms are optimized, For linear time-in variant (LTI) plants with unmodeled dynamics belonging to certain type s of prior unstructured uncertainty sets, upper and lower bounds of th e persistent identification measures are explicitly computed, It is sh own that when prior unmodeled dynamics are balls in the l(1) space, th e lower and upper bounds coincide, In this case, any full-rank periodi c probing signals are optimal, and the standard least-squares estimati on is in fact an optimal identification algorithm. Motivated by closed -loop identification problems, the concept of nearly periodic signals is introduced, It is shown that such signals are asymptotically optima l for persistent identification and at the same time can be generated in a closed-loop configuration, For slowly varying systems, the persis tent identification measures are shown to be continuous functions of t he plant variation rates. Furthermore, periodic signals are asymptotic ally optimal in the sense that they achieve identification errors whic h approach the optimal persistent identification errors for LTI system s when the variation rates of the plants become small. This result ver ifies that the persistent identification measures are indeed benchmark values for the identification of time-varying systems.