Adaptation in Stochastic Dynamic Systems—Survey and New Results II

Abstract

This paper surveys the field of adaptation in stochastic systems as it has developed over the last four decades. The author's research in this field is summarized and a novel solution for fitting an adaptive model in state space (instead of response space) is given.

Adaptation in Stochastic Dynamic Systems—Survey and New Results IV: Seeking Minimum of API in Parameters of Data

“…constitute the experimental condition (cf. Ljung [4]). X By assumption, is generated by the completely observable PhDM (2), so we can move from the physical state variables in (2) to another m t y R…”

“…with the initial 0 0 0 x x  , which is equivalent to (6), can be used where t t x is the optimal "filtered" estimator for t x based on experimental condition (4). When X  ranges (or switches) over  as in (1), we obtain the set of Kalman filters…”

“…In contrast to our previous work [2], we do not consider the four levels of uncertainty. Assume that system (2) (and also the SODM (5)) is parameterized by an lcomponent vector  of unknown system parameters, which needs to be identified.…”

“…The recent papers [1,2] gave a survey of the field of adaptation in stochastic systems as it has developed over the last four decades. The author's research in this field was summarized and a novel solution for fitting an adaptive model in state space (instead of response space) was given.…”

“…

This paper investigates the problem of seeking minimum of API (Auxiliary Performance Index) in parameters of Data Model instead of parameters of Adaptive Filter in order to avoid the phenomenon of over parameterization. This problem was stated by Semushin in [2]. The solution to the problem can be considered as the development of API approach to parameter identification in stochastic dynamic systems.

…”