Robust Stabilization of Uncertain Time-Delay Systems With Fractional Stochastic Noise Using the Novel Fractional Stochastic Sliding Approach and Its Application to Stream Water Quality Regulation

Khandani, Khosro; Majd, Vahid Johari; Tahmasebi, Mahdieh

doi:10.1109/tac.2016.2594261

Cited by 38 publications

(20 citation statements)

References 42 publications

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“…[18][19][20][21][22][23] The above results were the studies of deterministic system. However, in practical applications, many process can be regarded as stochastic nonlinear systems, such as stream water quality regulation, 24 rigid-flexible wing system 25 and et al Therefore, it is significant and imperative to research the adaptive problems for the stochastic systems. In Reference 9, an adaptive fuzzy finite time controller was designed for multi-input and multi-output stochastic nonlinear systems with non-triangular structure and unmeasured states on the basis of FLS and finite time stability.…”

Section: Introductionmentioning

confidence: 99%

Adaptive fixed‐time tracking control for stochastic pure‐feedback nonlinear systems

Liang

Hou

2021

Adaptive Control & Signal

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The article discusses the adaptive fixed-time control problems for the stochastic pure-feedback nonlinear systems. Different from the existing results, the priori information of unknown virtual control coefficients (UVCC) is no longer needed in this article, which is realized by emplying the bound estimation method and well-defined smooth functions. A novel semi-global practical fixed-time stability criterion for the stochastic nonlinear systems is presented. Correspondingly, a new construction of Lyapunov function is proposed for the nonlinear stochastic system by adding the lower bounds of the UVCC. Based on the fuzzy logical system and fixed time stability theorem, a novel adaptive fuzzy fixed-time tracking control algorithm for stochastic nonlinear system is raised firstly. By theoretical analysis, we can conclude that the whole variables of the controlled system are bounded almost surely and the output can track the desired reference signal to a very small compact set within a predefined fixed-time interval. Finally, the raised method is illustrated by two simulation examples.

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Section: Introductionmentioning

confidence: 99%

Adaptive fixed‐time tracking control for stochastic pure‐feedback nonlinear systems

Liang

Hou

2021

Adaptive Control & Signal

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“…FBMs now have been extensively used to model the stochastic perturbations as the input noise in dynamical systems. [13][14][15][16][17][18][19] For example, the integral sliding mode control for uncertain stochastic time-delay systems driven by FBMs was considered and a Lyapunov function with exponential term was proposed in Reference 14. Then the criterion of stochastic stability proposed in Reference 14 was not related to the Hurst index of FBMs.…”

Section: Introductionmentioning

confidence: 99%

Quantized feedback control for Markovian jumping singular systems driven by fractional Brownian motions

Xie

Meng

Kao

et al. 2021

Intl J Robust & Nonlinear

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The quantized feedback control for a type of delayed Markovian jumping singular systems driven by fractional Brownian motions is investigated. Firstly, the input is quantized by a uniform operator consisting of a linear part to deal with system stochastic stability and a nonlinear part to deal with the error caused by the quantizer. Secondly, to deal with the boundedness of fractional Brownian motions, a new type of Lyapunov function dependent of Hurst index is constructed. Then, utilizing generalized Finsler lemma and Gronwall inequality, some new criteria on the singular stochastic finite-time boundedness are obtained for the considered systems with the designed quantized input. Finally, a numerical example and a DC motor example are presented to verify the effectiveness of the proposed methods and results.

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“…Stability and stabilization of MJSs (Ali et al, 2019), ﬁltering (Li and Wang, 2012; Peng et al, 2019), and controller design for MJSs (Fei et al, 2017; Hou and Sun, 2018; Ma et al, 2018) have been well addressed in the literature. In recent years, SMC as a powerful robust method has been applied to different classes of fractional-order systems such as time-delay fractional order systems (Yousefi and Binazadeh, 2018), fractional-order chaotic systems (Roohi et al, 2019), fractional stochastic systems (Khandani et al, 2016, 2017) and so on. SMC has also been widely applied to MJSs; see Chen et al (2011), Jiang et al (2019), Kao et al (2014), Shen et al (2018), Zhang et al (2012), Zhao et al (2019) and the references therein.…”

Section: Introductionmentioning

confidence: 99%

A non-fragile observer-based adaptive sliding mode control for fractional-order Markovian jump systems with time delay and input nonlinearity

Parvizian

Khandani

Majd

2020

Transactions of the Institute of Measurement and Control

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In this paper, state estimation and adaptive sliding mode control (SMC) of uncertain fractional-order Markovian jump systems (FO-MJSs) with time delay and input nonlinearity are considered. A non-fragile observer is proposed to estimate the system states, and an observer-based adaptive sliding mode controller is synthesized to ensure the reachability of the sliding surfaces in the state-estimation space in finite time. The sufficient condition for stochastic stability of the error system and sliding mode dynamics is derived in the form of linear matrix inequalities (LMIs). Finally, some numerical examples are presented to illustrate the effectiveness of the proposed method.

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Robust Stabilization of Uncertain Time-Delay Systems With Fractional Stochastic Noise Using the Novel Fractional Stochastic Sliding Approach and Its Application to Stream Water Quality Regulation

Cited by 38 publications

References 42 publications

Adaptive fixed‐time tracking control for stochastic pure‐feedback nonlinear systems

Adaptive fixed‐time tracking control for stochastic pure‐feedback nonlinear systems

Quantized feedback control for Markovian jumping singular systems driven by fractional Brownian motions

A non-fragile observer-based adaptive sliding mode control for fractional-order Markovian jump systems with time delay and input nonlinearity

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