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A new theoretical and algorithmical basis for estimation, identification and control. (English) Zbl 0608.93002
A new theory applicable to data treatment is briefly exposed. This (gnostical) theory derives a mathematical model of data disturbed by uncertainly, the statistical model of which may be unknown or even unjustifiable. Gnostical theory is based on two simple axioms. It results in laws governing the uncertainty of each individual datum such as variational principles of virtual kinematics of real data and of their dynamics, closely related to entropy and information of data. Algorithms resulting from gnostical theory maximize the information obtained from data and yield data characteristics robust with respect to outlying or inlying data. Fields of application include the estimation of both location and scale parameters of small data samples and of their generalized correlations, robust estimation of probability and of probability distribution, non-linear discrete filtering, prediction and smoothing, identification of systems strong disturbances and adaptive setting of alarm systems, robust identification of regression models, robust control, cluster analysis etc.
Reviewer: J.Just

MSC:
93A05 Axiomatic systems theory
68U20 Simulation (MSC2010)
93E10 Estimation and detection in stochastic control theory
62H30 Classification and discrimination; cluster analysis (statistical aspects)
93B30 System identification
93B35 Sensitivity (robustness)
93C40 Adaptive control/observation systems
93E11 Filtering in stochastic control theory
93E12 Identification in stochastic control theory
62M20 Inference from stochastic processes and prediction
94A15 Information theory (general)
93E14 Data smoothing in stochastic control theory
93E25 Computational methods in stochastic control (MSC2010)
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References:
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