Asymptotic stabilization of continuous-time periodic stochastic systems by feedback control based on periodic discrete-time observations

Dong, Ran and Mao, Xuerong (2020) Asymptotic stabilization of continuous-time periodic stochastic systems by feedback control based on periodic discrete-time observations. Mathematical Control and Related Files, 10 (4). pp. 715-734. ISSN 2156-8499 (https://doi.org/10.3934/mcrf.2020017)

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Abstract

In 2013, Mao initiated the study of stabilization of continuoustime hybrid stochastic differential equations (SDEs) by feedback control based on discrete-time state observations. In recent years, this study has been further developed while using a constant observation interval. However, time-varying observation frequencies have not been discussed for this study. Particularly for non-autonomous periodic systems, it’s more sensible to consider the timevarying property and observe the system at periodic time-varying frequencies, in terms of control efficiency. This paper introduces a periodic observation interval sequence, and investigates how to stabilize a periodic SDE by feedback control based on periodic observations, in the sense that, the controlled system achieve Lp-stability for p > 1, almost sure asymptotic stability and pth moment asymptotic stability for p ≥ 2. This paper uses the Lyapunov method and inequalities to derive the theory. We also verify the existence of the observation interval sequence and explains how to calculate it. Finally, an illustrative example is given after a useful corollary. By considering the time-varying property of the system, we reduce the observation frequency dramatically and hence reduce the observational cost for control.

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