Mathematical theory of adaptation and the uniform ergodic theorem for operators in a B-lattice. (English. Russian original) Zbl 0668.93066

Sov. Phys., Dokl. 32, No. 7, 536-538 (1987); translation from Dokl. Akad. Nauk SSSR 295, 303-307 (1987).
We introduce the mathematical theory of adaptation in the framework of system theory in discrete time and state a theorem which makes it possible to effectively investigate all the aspects of some adaptation and learning models [see R. R. Bush and F. Mosteller, Stochastic models for learning (Russian) (Moscow 1962); for a review of the English original see Zbl 0064.390)] and to solve other problems in stochastic systems theory.


93E03 Stochastic systems in control theory (general)
93C55 Discrete-time control/observation systems
68T05 Learning and adaptive systems in artificial intelligence
93C40 Adaptive control/observation systems


Zbl 0064.390