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STRONG PREDICTOR-CORRECTOR APPROXIMATION FOR STOCHASTIC DELAY DIFFERENTIAL EQUATIONS

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Journal of Computational Mathematics 2015年第6期33卷 587-605页

作者： Yuanling Niu Chengjian Zhang Kevin Burrage School of Mathematics and Statistics Central South University Changsha 410075 China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China School of Mathematics and Statistics Huazhong University of Science and Technology Wuhan 430074 China Department of Computer Science Oxford University Wolfson Building Parks Road Oxford OX1 3QD UK School of Mathematical Sciences Queensland University of Technology Brisbane Australia

This paper presents a strong predictor-corrector method for the numerical solution of stochastic delay differential equations （SDDEs） of ItS-type. The method is proved to be mean-square convergent of order min{1/2,p} under the Lipschitz condition and the linear growth condition, where p is the exponent of HSlder condition of the initial function. stability criteria for this type of method are derived. It is shown that for certain choices of the flexible parameter p the derived method can have a better stability property than more commonly used numerical methods. That is, for some p, the asymptotic MS-stability bound of the method will be much larger than that of the Euler-Maruyama method. Numerical results are reported confirming convergence properties and comparing stability properties of methods with different parameters p. Finally, the vectorised simulation is discussed and it is shown that this implementation is much more efficient.

关键词： Strong predictor-corrector approximation Stochastic delay differential equa- tions Convergence mean-square stability Numerical experiments Vectorised simulation.

General Modified Split-Step Balanced Methods for Stiff Stochastic Differential Equations

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Journal of Donghua University(English Edition) 2013年第3期30卷 189-196页

作者：殷政伟甘四清李荣德 School of Mathematics and Statistics Henan University of Science and Technology State Key Laboratory of High Performance Complex Manufacturing School of Mathematics and StatisticsCentral South University CITIC Heavy Industries Co. LTD.

A class of general modified split-step balanced methods proposed in the paper can be applied to solve stiff stochastic differential systems with m-dimensional multiplicative noise. Compared to some other already reported split-step balanced methods, the drift increment function of the methods can be taken from any chosen ane-step ordinary differential equations （ODEs） solver. The schemes is proved to be strong convergent with order one. For the mean-square stability analysis, the investigation is confined to two cases. Some numerical experiments are reported to testify the performance and the effectiveness of the methods.

关键词： split-step balanced methods stiff stochastic differential equations strong convergence mean-square stability

Model Predictive Tracking Control for Networked Control Systems subject to Markovian Packet Dropout

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Model Predictive Tracking Control for Networked Control Syst...

第36届中国控制会议

作者： Jimin Yu Chunhua Kuang Xiaoming Tang College of Automation Chongqing University of Posts and Telecommunications Key Laboratory of Industrial Internet of Things & Networked Control Ministry of Education

ISBN: (纸本)9781538629185

This paper investigates the Robust model predictive tracking control for constrained networked control systems with Markovian packet dropout. By introducing a packet dropout compensation strategy and an augmented Markov jump linear model with polytopic uncertainties, the effects of data loss on the system performance are considered simultaneously. Input, and output constraints are also incorporated into the model predictive control. Furthermore, both the recursive feasibility of the proposed MPC algorithm and the closed-loop mean-square stability are proved. A numerical example is given to illustrate the effectiveness of the controller.

关键词： NCS model predictive tracking control Markovian packet dropout recursive feasibility mean-square stability

Moment Equations of Linear It Stochastic Systems with Applications

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Journal of Systems Engineering and Electronics 1998年第2期9卷 1-7页

作者： Deng Feiqi Liu Hongwei Feng Zhaoshu & Liu Yongqing(Department of Automatic Control Engineering, South China University of Technology,Guangzhou 510641, P. R. China)

In this paper, with the Kronecker's product and Kronecker's sum of matrices, the 2nd order moment equations of linear Ito stochastic systems are dervided. Based on the moment equations obtained, a necessary and sufficient condition for the mean-square asymptotic stability of linear Ito stochastic systems is *** the time-invariant stochastic systems,the necessary and sufficient condition is just the same as the Hurwitz property of certain matrices related to the coefficient matrices of the systems. An algorithm STILSS is given for testing the mean-square asymptotic stability of time-invariant linear Ito stochastic systems.

关键词： Moment equations mean-square stability Necessary and sufficient condition Algorithm

一种四级半隐式随机Runge-Kutta方法

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高等学校计算数学学报 2013年第1期35卷 28-39页

作者：严刚峰黄显核成都大学电子信息工程学院电子科技大学自动化工程学院

1引言对于大多数的工程实际问题,一般都是采用确定性微分方程来描述和研究的.然而在工程实际中,含有随机因素是不可避免的.如果仍然采用确定性微分方程来研究,那么只有对相应的微分方程进行摄动,或者其它的近似方法来分析.要想更加准确... 详细信息

1引言对于大多数的工程实际问题,一般都是采用确定性微分方程来描述和研究的.然而在工程实际中,含有随机因素是不可避免的.如果仍然采用确定性微分方程来研究,那么只有对相应的微分方程进行摄动,或者其它的近似方法来分析.要想更加准确地研究含随机现象的工程实际问题,还是要对建立的确定性模型引入随机项,进而建立相应的随机微分方程,并进行求解.但是除了极少数类型的线性方程可以得到解析解.绝大多数的随机微

关键词： Stratonovich stochastic differential equations bi-colored rooted Runge-Kutta method mean-square stability

Quantized Control for Stochastic System

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Quantized Control for Stochastic System

第三十届中国控制会议

作者： WEI Li~1,ZHANG Huanshui~1,FU Minyue~2 1.School of Control Science and Engineering,Shandong University,Jingshi Road,Jinan 17923,P.R.China. 2.School of Electrical Engineering and Computer Science,The University of Newcastle,NSW 2308,Callaghan,Australia

＜正＞This paper considers the coarsest quantization control *** from the previous works[4]where the systems are restricted to be deterministic,we focus on the feedback quantization control for general stochastic systems with multiplicative *** is showed that the coarsest quantizer that stabilize the multiplicative-noise stochastic system in mean-square sense is logarithmic,and the quantization density of which is larger than the results obtained in[4]for deterministic systems for the deterioration of multiplicative ***,we explore that the solvability of the quantizer density is related to a special stochastic linear control problem.

关键词： mean-square stability Stochastic Multiplicative Noise Quantization Feedback Control

State Feedback Controller Design of Networked Control Systems With Multiple Packet Dropouts

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State Feedback Controller Design of Networked Control System...

第二十九届中国控制会议

作者： ZHANG Changzhu1,FENG Gang1,GAO Huijun2,ZHAO Yan2 1.Department of manufacturing Engineering and Engineering Management,City University of Hong Kong,Kowloon,Hong Kong,P.R.China2.Space Control and Inertial Technology Research Center,Harbin Institute of Technology,Harbin,Heilongjiang Province,150001,P.R.China

This paper presents a kind of controller design method for a class of networked control systems（NCSs）with multiple packet dropouts,where the number of consecutive packet dropouts is limited by a known upper bound.A novel model that can be used to describe multiple packet dropouts in both sensor-to-controller and controller-to-actuator sides is provided.A sufficient condition for mean-square asymptotic stability is derived for the closed-loop networked control system,which is dependent on the upper bound of the packet dropouts *** corresponding state feedback control law is presented in terms of linear matrix inequalities（LMIs）.A networked control system for an inverted pendulum is finally provided to show the effectiveness and applicability of the proposed method.

关键词： LMIs mean-square stability Networked control systems Packet dropouts

Indefinite Stochastic Linear Quadratic Control in Infinite Time Horizon

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Indefinite Stochastic Linear Quadratic Control in Infinite T...

第二十六届中国控制会议

作者： Tang Huaibin1,Wu Zhen1,Zhang Weihai2 1.School of Mathematics and System Sciences,Shandong University,Jinan 250100,P.R.China2.College of Mechanical and Eletrical Engineering,Shandong Institute of Light Industry,Jinan 250000,P.R.China

In this paper,we will be concerned with an optimal stochastic linear-quadratic（LQ in short）control problem in an infinite time horizon,where the cost matrices are allowed to be *** which,a generalized algebraic Riccati equation（GARE in short）which involves a matrix pseudoinverse is *** some stabilizing conditions,we establish the relation between the solvability of the GARE and the existence of the optimal controls of the LQ control *** on this relation,the optimal controls can be constructed by the solution of the GARE if it ***,we give a sufficient condition for the solvability of the GARE based on the semidefinite programming.

关键词： Stochastic linear-quadratic control Generalized algebraic Riccati equation Linear matrix inequality mean-square stability Semidefinte programming