Stabilisation of hybrid stochastic differential equations by feedback control based on discrete‐time observations of state and mode

Abstract

This version is available at https://strathprints.strath.ac.uk/58494/ Strathprints is designed to allow users to access the research output of the University of Strathclyde. Unless otherwise explicitly stated on the manuscript, Copyright © and Moral Rights for the papers on this site are retained by the individual authors and/or other copyright owners. Please check the manuscript for details of any other licences that may have been applied. You may not engage in further distribution of the material for any profitmaking activities or any commercial gain. You may freely distribute both the url (https://strathprints.strath.ac.uk/) and the content of this paper for research or private study, educational, or not-for-profit purposes without prior permission or charge.Any correspondence concerning this service should be sent to the Strathprints administrator: strathprints@strath.ac.ukThe Strathprints institutional repository (https://strathprints.strath.ac.uk) is a digital archive of University of Strathclyde research outputs. It has been developed to disseminate open access research outputs, expose data about those outputs, and enable the management and persistent access to Strathclyde's intellectual output. (SDEs) by the feedback controls based on the discrete-time observations of the state. However, the feedback controls still depend on the continuous-time observations of the mode. Of course this is perfectly fine if the mode of the system is obvious (i.e. fully observable at no cost). However, it could often be the case where the mode is not obvious and it costs to identify the current mode of the system. To reduce the control cost, it is reasonable we identify the mode at the discrete times when we make observations for the state. Hence the feedback control should be designed based on the discrete-time observations of both state and mode. The aim of this paper is to show how to design such a feedback control to stabilise a given hybrid SDE. Stabilisation of Hybrid Stochastic Differential Equations by Feedback Control based on Discrete-time Observations of State and Mode

Aperiodically intermittent stochastic stabilization via discrete time or delay feedback control

“…., where τ is the duration time of every observation. Hence, many discrete time feedback control techniques have been proposed and discussed by several authors [20][21][22][23][24]. It is worth pointing out that Mao and his collaborators [25,26] combined stochastic stabilization technology with discrete-time feedback control or time-delay feedback control techniques respectively, and they have stabilized an unstable system via discrete-time observation noise or delay time observation noise.…”

Almost sure stabilization of hybrid systems by feedback control based on discrete-time observations of mode and state

“…On the other hand, a better bound on τ * was also obtained in [32] by making use of Lyapunov functionals. In particular, Song et al [33] pointed out that the discrete-time feedback control in controlled hybrid stochastic systems was based on not only the discrete-time observations of the state, x(kτ ) (k = 0, 1, 2, . .…”

Robust quantised control of hybrid stochastic systems based on discrete-time state and mode observations

“…The stabilization problem of continuous-time hybrid stochastic systems has already been discussed in, for example, [12][13][14][15][16][17]. The mean-square exponential stabilization of the hybrid systems by delay feedback control was proposed in [12].…”

“…In [16], the method of the Lyapunov functionals was introduced to study the mean square stability and the almost sure stability. More recently, [17] took a further step to investigate the issue of feedback control based on discrete-time observations of both state and mode.…”