Stabilisation of highly nonlinear hybrid systems by feedback control based on discrete-time state observations

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Fei, Chen and Fei, Weiyin and Mao, Xuerong and Xia, Dengfeng and Yan, Litan (2020) Stabilisation of highly nonlinear hybrid systems by feedback control based on discrete-time state observations. IEEE Transactions on Automatic Control, 65 (7). 2899 - 2912. ISSN 0018-9286 (https://doi.org/10.1109/TAC.2019.2933604)

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Abstract

Given an unstable hybrid stochastic differential equation (SDE), can we design a feedback control, based on the discrete-time observations of the state at times 0, τ, 2τ, · · · , so that the controlled hybrid SDE becomes asymptotically stable? It has been proved that this is possible if the drift and diffusion coefficients of the given hybrid SDE satisfy the linear growth condition. However, many hybrid SDEs in the real world do not satisfy this condition (namely, they are highly nonlinear) and there is no answer to the question yet if the given SDE is highly nonlinear. The aim of this paper is to tackle the stabilization problem for a class of highly nonlinear hybrid SDEs. Under some reasonable conditions on the drift and diffusion coefficients, we show how to design the feedback control function and give an explicit bound on τ (the time duration between two consecutive state observations), whence the new theory established in this paper is implementable.

ORCID iDs

Fei, Chen, Fei, Weiyin, Mao, Xuerong ORCID logoORCID: https://orcid.org/0000-0002-6768-9864, Xia, Dengfeng and Yan, Litan;
  • Item type:Article
    ID code:69146
    Dates:
    Date
    Event
    31 July 2020
    Published
    6 August 2019
    Published Online
    30 July 2019
    Accepted
    Notes:© 2019 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
    Subjects:Science > Mathematics
    Department:Faculty of Science > Mathematics and Statistics
    Depositing user: Pure Administrator
    Date deposited:31 Jul 2019 10:29
    Last modified:19 Dec 2024 01:23
    URI:https://strathprints.strath.ac.uk/id/eprint/69146
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