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Adaptive control for time‐varying systems: A combination of Martingale and Markov chain techniques
Author(s) -
Guo Lei,
Meyn Sean P.
Publication year - 1989
Publication title -
international journal of adaptive control and signal processing
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.73
H-Index - 66
eISSN - 1099-1115
pISSN - 0890-6327
DOI - 10.1002/acs.4480030102
Subject(s) - control theory (sociology) , markov chain , martingale (probability theory) , kalman filter , a priori and a posteriori , mathematics , mathematical optimization , computer science , statistics , control (management) , philosophy , epistemology , artificial intelligence
Abstract Adaptive control problems of a first‐order randomly time‐varying stochastic system are considered. A class of adaptive controllers based on the Kalman filter is introduced and is analysed using a combination of martingale and Markov chain techniques. It is shown that both the expected value and sample path averages of the square of the output of the closed‐loop system remain bounded and that the long‐run cost is a continuous functional of the parameters of the controller and the distribution of the disturbance process. These results hold even when the Gaussian assumption used in previous papers is removed and the a priori estimate of the noise variance is incorrect.