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On the steady state behaviour of stochastic systems
Author(s) -
Caines P. E.,
Meynt S. P.,
Moscas E.
Publication year - 1988
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.4480020205
Subject(s) - ergodic theory , markov process , steady state (chemistry) , mathematics , invariant (physics) , stochastic process , control theory (sociology) , state (computer science) , statistical physics , control (management) , computer science , mathematical analysis , physics , statistics , chemistry , algorithm , artificial intelligence , mathematical physics
The question of the existence of steady state solutions to the closed loop system equations for stochastic systems, and in particular ARMAX systems under non‐linear feedback control, is addressed. Using the ergodic theory of time‐invariant Markov processes, it is shown that corresponding to a large class of control laws there exist shift‐invariant probabilities for the joint disturbance input‐output processes. This permits an asymptotic analysis of (i) averages of functions of the state process, (ii) the probability distributions governing the state process and (iii) loss functions on the system in the steady state.