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Best performance analysis for stochastic perturbation systems with spectral factorization

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Journal of Shanghai University(English Edition) 2008年第1期12卷 80-84页

作者：王建国曹广益朱新坚 Department of Automation School of Electronic Information and Electrical Engineering Shanghai Jiaotong University Shanghai 200030 P. R. China

We investigate the best performance for linear feedback control systems in the case that plant uncertainty is to be considered. First, we define an average integral square criterion of tracking error over a class of stochastic model errors. By utilizing spectral factorization to minimize the performance index, we derive an optimal controller design method and further study best performance in the presence of stochastic perturbation. The results can be used to evaluate optimal performance in practical control system designs.

关键词： best tracking plant uncertainty stochastic perturbation spectral factorization

Tracking Control for Helicopters with Input stochastic perturbation

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Tracking Control for Helicopters with Input Stochastic Pertu...

Persistence and periodic measure of a stochastic predator-prey model with Beddington-DeAngelis functional response

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作者： Yankai Li Mou Chen Jianye Liu College of Automation Engineering Nanjing University of Aeronautics and Astronautics

In this paper, the flight control problem for helicopters is investigated under input stochastic perturbation.The unmeasurable states of the helicopter are estimated by a state observer. Then, combining the estimated states with the other measurable states of the helicopter, a state feedback controller is designed. In the controller design, the input stochastic perturbation is considered. By applying the designed controller, the helicopter is maintaining a hovering state at the predefined positions and yaw angle. In order to guarantee the stochastic stability of the closed-loop system, a sufficient condition is presented by using the theory of stochastic differential equation, Lyapunov stability method and linear matrix inequalities（LMIs） technique. Finally, the simulation is given to show the effectiveness of the proposed results.

关键词： Helicopter state observer stochastic perturbation linear matrix inequalities hovering

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生物数学学报:英文版 2023年第6期16卷 175-207页

作者： Jiangtao Yang School of Mathematics and Statistics Yangtze Normal UniversityChongqing408100P.R.China

In this paper,we study a stochastic predator-prey model with Beddington-DeAngelis functional response and time-periodic coefficients.By analyzing the stability of the solution on the boundary and some stochastic estimates,the threshold conditions for the time-average persistence in probability and extinction of each population are established.Furthermore,the existence of a unique periodic measure of the model is also presented under the condition of the time-average persistence in probability of the model.Several numerical simulations are given to verify the effectiveness of the theoretical results and to illustrate the effects of the white noises on the persistence and periodic measure of the model.

关键词： Predator-prey model stochastic perturbation persistence extinction periodic measure

Stationary distribution and probability density function of a stochastic waterborne pathogen model with logistic growth

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生物数学学报:英文版 2023年第8期16卷 191-229页

作者： Yue Liu Jize Wei Department of Mathematics City University of Hong Kong Tat Chee Avenue KowloonHong KongP.R.China Department of Applied Mathematics The Hong Kong Polytechnic University Hung Hom KowloonHong KongP.R.China

Waterborne disease threatens public health globally.Previous studies mainly consider that the birth of pathogens in water sources arises solely by the shedding of infected individuals,However,for free-living pathogens,intrinsic growth without the presence of hosts in environment could be possible.In this paper,a stochastic waterborne disease model with a logistic growth of pathogens is investigated.We obtain the sufficient conditions for the extinction of disease and also the existence and uniqueness of an ergodic stationary distribution if the threshold R_(0)^(s)>1.By solving the Fokker-Planck equation,an exact expression of probability density function near the quasi-endemic equilibrium is obtained.Results suggest that the intrinsic growth in bacteria population induces a large reproduction number to determine the disease dynamics.Finally,theoretical results are validated by numerical examples.

关键词： Waterborne pathogen logistic growth stochastic perturbation Fokker-Planck equation density function

stochastic optimal control for norovirus transmission dynamics by contaminated food and water

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Chinese Physics B 2022年第2期31卷 173-188页

作者： Anwarud Din 黎永锦 Department of Mathematics Sun Yat-sen UniversityGuangzhou 510275China

Norovirus is one of the most common causes of viral gastroenteritis in the world,causing significant morbidity,deaths,and medical costs.In this work,we look at stochastic modelling methodologies for norovirus transmission by water,human to human transmission and food.To begin,the proposed stochastic model is shown to have a single global positive solution.Second,we demonstrate adequate criteria for the existence of a unique ergodic stationary distribution R0 s>1 by developing a Lyapunov function.Thirdly,we find sufficient criteria Rsstochastic control problems to regulate the spread of the disease using some external measures.Additional graphical solutions have been produced to further verify the acquired analytical results.This research could give a solid theoretical foundation for understanding chronic communicable diseases around the world.Our approach also focuses on offering a way of generating Lyapunov functions that can be utilized to investigate the stationary distribution of epidemic models with nonlinear stochastic disturbances.

关键词： stochastic norovirus model stochastic transmission stochastic perturbation stochastic stability stochastic optimal control

Finite-time control for a class of hybrid systems via quantized intermittent control

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Science China(Information Sciences) 2020年第9期63卷 140-155页

作者： Xiaolin XIONG Xinsong YANG Jinde CAO Rongqiang TANG Cunjin College Guangdong Ocean University School of Mathematical Sciences Chongqing Normal University Key Laboratory of Optimization and Control Ministry of Education School of Mathematics and Research Center for Complex Systems and Network SciencesSoutheast University

This paper considers the finite-time drive-response synchronization of stochastic nonlinear systems consisting of continuous-time and discrete-time subsystems. To save communication resources and reduce control cost, quantized controllers, which only work on continuous-time intervals, are designed. Owing to the hybrid characteristics of continuous-and discrete-time subsystems, existing finite-time stability theorems are not applicable. By developing novel analytical techniques, three criteria are derived to guarantee the finite-time synchronization. Moreover, the settling time is explicitly estimated. It is shown that the settling time is dependent not only on the control gains and systems’ initial conditions, but also on the control width and uncontrolled width. Numerical examples demonstrate the effectiveness of the theoretical analysis.

关键词： hybrid system finite-time synchronization quantized intermittent control stochastic perturbation

Adaptive stochastic Synchronization of Uncertain Delayed Neural Networks

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Journal of Applied Mathematics and Physics 2023年第9期11卷 2533-2544页

作者： Enli Wu Yao Wang Fei Luo College of Mathematics and Statistics Sichuan University of Science and Engineering Zigong China

This paper considers adaptive synchronization of uncertain neural networks with time delays and stochastic perturbation. A general adaptive controller is designed to deal with the difficulties deduced by uncertain parameters and stochastic perturbations, in which the controller is less conservative and optimal since its control gains can be automatically adjusted according to some designed update laws. Based on Lyapunov stability theory and Barbalat lemma, sufficient condition is obtained for synchronization of delayed neural networks by strict mathematical proof. Moreover, the obtained results of this paper are more general than most existing results of certainly neural networks with or without stochastic disturbances. Finally, numerical simulations are presented to substantiate our theoretical results.

关键词： Neural Networks Synchronization Time Delays stochastic perturbation Adaptive Control

Some Further Results on Fixed-Time Synchronization of Neural Networks with stochastic perturbations

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Journal of Applied Mathematics and Physics 2022年第1期10卷 200-218页

作者： Aminamuhan Abudireman Mairemunisa Abudusaimaiti Wanjuan Sun Jiangyuan Zhao Yuanshuang Zhang Abdujelil Abdurahman College of Mathematics and System Sciences Xinjiang University Urumqi China

In this paper, fixed-time (FXT) synchronization issue of a type of neural networks (NNs) with stochastic perturbations is considered. First, we obtained some novel sufficient criteria to guarantee the FXT synchronization of considered networks via introducing two types of controllers and employing some inequality techniques. Lastly, our theoretical results are verified via giving two numerical examples with their Matlab simulations.

关键词： Fixed-Time Stability stochastic perturbation Synchronization Neural Network

stochastic dynamics of the transmission of Dengue fever virus bet ween mosquit oes aiul humans

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International Journal of Biomathematics 2021年第7期14卷 329-352页

作者： Manjing Guo Lin Hu Lin-bei Nie College of Mathematics and System Science Xinjiang University Urumqi830046P.R.China

Considering the impact of environmental white noise on the quantity and behavior ofvector of disease,a stochastic differential model describing the transmission of Denguefever between mosquitoes and humans,in this paper,is proposed.By using Lyapunovmethods and Ito's formula,we first prove the existence and uniqueness of a globalpositive solution for this model.Further,some sufficient conditions for the extinction andpersistence in the mean of this stochastic model are obtained by using the techniquesof a series of stochastic inequalities.In addition,we also discuss the existence of aunique stationary distribution which leads to the stochastic persistence of this disease.Finally,several numerical simulations are carried to illustrate the main results of thiscontribution.

关键词： Dengue model stochastic perturbation persistence and extinction in the mean stationary distribution