Adaptation in Stochastic Dynamic Systems—Survey and New Results I

Abstract

This paper surveys the field of adaptation mechanism design for uncertainty parameter estimation as it has developed over the last four decades. The adaptation mechanism under consideration generally serves two tightly coupled functions: model identification and change point detection. After a brief introduction, the paper discusses the generalized principles of adaptation based both on the engineering and statistical literature. The stochastic multiinput multioutput (MIMO) system under consideration is mathematically described and the problem statement is given, followed by a definition of the active adaptation principle. The distinctive property of the principle as compared with the Minimum Prediction Error approach is outlined, and a plan for a more detailed exposition to be provided in forthcoming papers is given.

Adaptation in Stochastic Dynamic Systems—Survey and New Results II

“…As assumed earlier [7], all data models     forming a set  are parameterized by an l-component vector θ. . Within  , a model switching mechanism exists.…”

“…Time has shown that the importance of the Ljungian concepts is greater. Thus each of the five generalized principles of stochastic system adaptation [7] worked out in correlation with Mehra's ideas on adaptive filtering [8], can also be perceived from this point of view. Among these is the Performance Index-based Adaptive Model Principle of Adaptation.…”

“…The key was to exploit the complete observability property of Data Source under consideration in such a way that a finite batch of DS responses t y to t s y  would give access to the unreachable DS state (the dashed arrow in Figure 3) against the background of independent noise. In that event Auxiliary Performance Index (API) to Original Performance Index o  could be formed to suite the principal requirement a o = const    as it was formulated in [7], and by doing so, to fit an adaptive model in state space.…”

“…System identification and adaptive control are deeply intertwined areas. Further still, the latter is unthinkable without the former being the central part of the triune "Classifier--Identifier--Modifier" whose presence in a system makes it adaptive, see Figure 4 reproduced below from [7] where, keeping in mind adaptive nature of Identifier and the modern identification for control paradigm [2], the name Adaptor is used.…”

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

“…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.…”