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Randomly Switching Systems:Models,Analysis,and Applications

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Randomly Switching Systems:Models,Analysis,and Applications

A PARALLEL ITERATIVE DOMAIN DECOMPOSITION ALGORITHM FOR ELLIPTIC PROBLEMS

2009中国控制与决策会议

作者： G.Yin~1,C.Zhu~2 1.department of mathematics,wayne state university,detroit,mi 48202,usa 2.department of Mathematical Sciences,university of Wisconsin-milwaukee,milwaukee,WI 53201,usa

＜正＞This work provides a survey on some of the recent progress of switching diffusion *** recent years,switching diffusion systems have gained much popularity owing to their flexibility in modeling and their nature to conveniently depict the coexistence of continuous dynamics and discrete *** this paper,we begin with a number of motivating examples to display a variety of applications that can be covered by switching *** we study several important properties of the underlying *** weak stability is treated,and then ergodicity is considered, which provides us with a useful tool to replace the time-varying system measures by an ergodic or limit *** for equilibria is also *** the totally degenerated diffusions（i.e.,no Gaussian noise case）,we are dealing with switched ordinary differential equations.A somewhat surprising discovery is an insight different from the well-know Hartman-Grobman theorem regarding *** approximation for the solution of controlled switching diffusions are also considered.

关键词： Switching diffusion weak stability stability ergodic measure stabilization numerical method numerical method for control problem.

来源： cnki会议评论

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Journal of Computational mathematics 1998年第2期16卷 141-151页

作者： Dao-qi Yang (department of mathematics, wayne state university, detroit, mi 48202, usa) wayne state Univ Dept Math Detroit MI 48202 USA

An iterative nonoverlapping domain decomposition procedure is proposed and analyzed for linear elliptic problems. At the interface of two subdomains, one subdomain problem requires that Dirichlet data be passed to it from the previous iteration level, while the other subdomain problem requires that Neumann data be passed to it. This procedure is suitable for parallel processing. A convergence analysis is established. Standard and mixed finite element methods are employed to give discrete versions of this domain decomposition algorithm. Numerical experiments arc conducted to show the effectiveness of the method.

关键词： Domain decomposition methods finite element methods parallel computing

Polynomials,Higher Order Sobolev Extension Theorems and Interpolation Inequalities on Weighted Folland-Stein Spaces on Stratified Groups

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Acta Mathematica Sinica,English Series 2000年第3期16卷 405-444页

作者： Guozhen Lu department of mathematics,wayne state university,detroit,mi 48202,usa department of mathematics Wayne State University Detroit USA

This paper consists of three main *** of them is to develop local and global Sobolev interpolation inequalities of any higher order for the nonisotropic Sobolev spaces on stratified nilpotent Lie *** the extensive research after Jerison’s work[3]on Poincaré-type inequalities for Hrmander’s vector fields over the years,our results given here even in the nonweighted case appear to be *** interpolation inequalities have crucial applications to subelliptic or parabolic PDE’s involving vector *** main tools to prove such inequalities are approximating the Sobolev func- tions by polynomials associated with the left invariant vector fields on *** very useful properties for polynomials associated with the functions are given here and they appear to have independent interests in their own *** the existence of such polynomials is the second main part of this *** results of these two parts have been announced in the author’s paper in Mathematical Research Letters[38]. The third main part of this paper contains extension theorems on anisotropic Sobolev spaces on stratified groups and their applications to proving Sobolev interpolation inequalities on(εδ)domains. Some results of weighted Sobolev spaces are also given *** construct a linear extension operator which is bounded on different Sobolev spaces *** particular,we are able to construct a bounded linear extension operator such that the derivatives of the extended function can be controlled by the same order of derivatives of the given Sobolev *** are stated and proved for weighted anisotropic Sobolev spaces on stratified groups.

关键词： Poincaré inequalities Extension theorems Interpolation inequalities Anisotropic Sobolev spaces A_p weights (ε,δ)domains Vector fields Polynomials on stratified groups

Occupation Measures of Singularly Perturbed Markov Chains with Absorbing states

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Acta Mathematica Sinica,English Series 2000年第1期16卷 161-180页

作者： G.Yin~(1)) department of mathematics,wayne state university,detroit,mi 48202,usaQ.Zhang~(2)) department of mathematics,university of Georgia,Athens,GA 30602,usaG.Badowski~(3)) department of mathematics,wayne state university,detroit,mi 48202,usa department of mathematics Wayne State University Detroit MI 48202 USA department of mathematics University of Georgia Athens GA 30602 USA

This paper develops asymptotic properties of singularly perturbed Markov chains with inclusion of absorbing *** focuses on both unscaled and scaled occupation *** mild conditions,a mean-square estimate is *** averaging the fast components,we obtain an aggregated *** the aggregated process itself may be non-Markovian,its weak limit is a Markov chain with much smaller state ***,a suitably scaled sequence consisting of a component of scaled occupation measures and a component of the aggregated process is shown to converge to a pair of processes with a switching diffusion component.

关键词： Singularly perturbed Markov chain Occupation measure Aggregation Absorbing state Weak convergence Switching diffusion

ON THE hp FINITE ELEMENT METHOD FOR THE ONE DIMENSIONAL SINGULARLY PERTURBED CONVECTION-DIFFUSION PROBLEMS

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Journal of Computational mathematics 2002年第6期20卷 599-610页

作者： Zhi-min Zhang (department of mathematics, wayne state university, detroit, mi 48202, U.S.A.) department of mathematics Wayne State University 美国 Detroit MI 48202

Presents information on singularly peturbed two-point boundary value problem of convection-diffusion type. Analysis of the problem; Details of an hp version finite element method on a strongly graded piecewise uniform... 详细信息

关键词： hp-version finite element methods convection-diffusion singularly perturbed exponential rate of convergence.

SIGNAL ESTIMATION WITH BINARY-VALUED SENSORS

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Journal of Systems Science & Complexity 2010年第3期23卷 622-639页

作者： Leyi WANG Gang George YIN Chanying LI Weixing ZHENG department of Electrical and Computer Engineering Wayne State University Detroit Michigan 48202 USA department of mathematics Wayne State University Detroit Michigan 48202 USA department of Mechanical Engineering The University of Hong Kong Pokfulam Road Hong Kong China School of Computing and mathematics University of Western Sydney Australia

This paper introduces several algorithms for signal estimation using binary-valued *** main idea is derived from the empirical measure approach for quantized identification,which has been shown to be convergent and asymptotically efficient when the unknown parametersare *** estimation under binary-valued observations must take into consideration oftime varying *** empirical measure based algorithms are modified with exponentialweighting and threshold adaptation to accommodate time-varying natures of the *** anyinformation on signal generators,the authors establish estimation algorithms,interaction between noisereduction by averaging and signal tracking,convergence rates,and asymptotic efficiency.A thresholdadaptation algorithm is *** convergence and convergence rates are analyzed by using theODE method for stochastic approximation problems.

关键词： Identification signal estimation.

VMckpt:lightweight and live virtual machine checkpointing

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Science China(Information Sciences) 2012年第12期55卷 2865-2880页

作者： LIU HaiKun 1,JIN Hai 1,LIAO XiaoFei 1,MA Bo 1 & XU ChengZhong 2 1 Services Computing Technology and System Lab,Cluster and Grid Computing Lab,School of Computer Science and Technology,Huazhong university of Science and Technology,Wuhan 430074,China 2 department of Electrical and Computer Engineering,wayne state university,detroit,mi 48202,usa 1. Services Computing Technology and System Lab Cluster and Grid Computing Lab School of Computer Science and Technology Huazhong University of Science and Technology Wuhan 430074 China2. Department of Electrical and Computer Engineering Wayne State University Detroit MI [48202 USA

Recent advance of virtualization technology provides a new approach to check-point/restart at the virtual machine(VM) *** contrast to traditional process-level checkpointing,checkpointing at the virtualization layer brings up several advantages,such as compatibility,transparence,flexibility and ***,because the virtualization layer has little semantic knowledge about the operation system and the applications running atop,VM-layer checkpointing requires saving the entire operating system state rather than a single *** overhead may render the approach *** reduce the size of VM checkpoint,in this paper we propose a page eviction scheme and an incremental checkpointing mechanism to avoid saving unnecessary VM pages in the *** keep the system online transparently,we propose a live checkpointing mechanism by saving the memory image in a copy-on-write(COW) *** implement the performance optimization mechanisms in a prototype system,called *** results with a group of representative applications show that our page eviction scheme and incremental checkpointing can significantly reduce the checkpoint file size by up to 87% and shorten the total checkpointing/restart time by a factor of up to 71%,in comparison with the Xens default checkpointing *** observed application downtimes due to checkpointing can be reduced to as small as 300 ms.

关键词： checkpoint/restart copy-on-write page eviction virtual machine

CONVERGENCE RATES OF MARKOV CHAIN APPROXIMATION METHODS FOR CONTROLLED DIFFUSIONS WITH STOPPING

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Journal of Systems Science & Complexity 2010年第3期23卷 600-621页

作者： Qingshuo SONG Gang George YIN department of mathematics City University of Hong Kong 83 Tat Chee Avenue Kowloon Tong Hong Kong China department of mathematics Wayne State University Detroit Michigan 48202 USA

This work is concerned with rates of convergence of numerical methods using Markov chainapproximation for controlled diffusions with stopping (the first exit time from a bounded region).In lieuof considering the associated finite difference schemes for Hamilton-Jacobi-Bellman (HJB) equations,a purely probabilistic approach is *** is an added difficulty due to the boundary condition,which requires the continuity of the first exit time with respect to the discrete *** prove theconvergence of the algorithm by Markov chain approximation method,a tangency problem might arise.A common approach uses certain conditions to avoid the tangency ***,by modifying thevalue function,it is demonstrated that the tangency problem will not arise in the sense of convergencein probability and in L^*** addition,controlled diffusions with a discount factor is also treated.

关键词： Controlled diffusion dynamic programming equation Markov chain approximation rate of convergence.

INFORMATION AND COMPLEXITY IN CONTROL SYSTEMS: A TUTORIAL

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Journal of Systems Science & Complexity 2001年第1期14卷 1-16页

作者： WANG Leyi (department of Electrical and Computer Engineering, wayne state university, detroit, michigan 48202, usa) wayne state university 美国 48202

This is a tutorial paper which presents schematically the concepts of information, uncertainty, and complexity, and their relationships in their applications to control systems. By focusing on exact or lower bounds on achievable performance in the presence of uncertainties, studies of complexity in a control system can potentially reveal fundamentally limiting factors of the system, suggest beneficial modifications to system structures and hardware configurations to remove these limitations, provide benchmark values for evaluating a design and for quantifying rooms for performance improvement, and demonstrate intrinsic tradeoffs. Compared to its counterparts in communications (Shannon’s information theory), computations (computational complexity and information-based complexity), and approxima- tions (n-widths and Kolmogorov entropy), studies of information and complexity in control systems encounter further challenges, such as characterization of feedback robustness, interaction between identification and control, and co-existence of deterministic and stochastic uncertainties. Some of these issues are outlined and discussed.

关键词： Information uncertainty complexity control identification.