Structural Equivalence of Topological Machines

Recently, there has been a fair amount of interest in the study of topological machines, e.g. Day [2], Norris [4] and Sikdar [5]. Due to the topological structures endowed in the input, output, and state spaces of the topological machines, most of the results of conventional deterministic machines do not admit of an immediate generalization to the topological case. In this paper, we shall study the structural equivalences of topological machines. Various concepts are defined including quotient submachines, irreducibility, reduced forms, homomorphisms, minimality, and minimal forms. It is shown that every topological machine has a unique reduced form and has a minimal form which is unique up to iseomorphism. Moreover, it is shown that a topological machine is irreducible if and only if it is minimal.     

Wilkie-Perkins low-order sensitivity model revisited

The minimality of the Wilkie-Perkins low-order sensitivity model [1] for multi-input systems is reexamined. An example is offered to provide insight into the optimality discussion of Guardabassi et al. [2]. Then it is indicated that generation of sensitivity functions of arbitrary multi-input systems requires at mostm . nintegrators in addition to the system model.     

Speech Modeling via Model Reduction

Using model reduction, a new approach for low-order speech modeling is presented. In this approach, the modeling process starts with a relatively high-order (full-order) autoregressive (AR) model obtained by some classical methods. The AR model is then reduced using the state projection method, operating in the state space. The model reduction yields a reduced-order autoregressive moving-average (ARMA) model that interestingly preserves the key properties of the original full-order model such as stability, minimality, and phase minimality. Line spectral frequencies (LSF) and signal-to-noise ratio (SNR) behavior are also investigated. To illustrate the performance and effectiveness of the proposed approach, some computer simulations were conducted on some practical speech segments.     

Minimal-order estimation of multivariable continuous time stochastic linear systems

Minimal-order state estimation of continuous time, multiinput, multioutput stochastic linear systems is considered. A necessary and sufficient condition for order minimality is obtained in terms of the internal system structure.     

Asymptotic Properties of Random Processes That Arise in Learning Models

This paper develops the properties of a stochastic learning model first reported in [1] and [2]. Some mathematical problems that appear to be interesting in themselves have arisen in the analysis of the limiting behavior of this stochastic model. Because of this these problems will be examined in a framework that is broader than that strictly required for model analysis.     

Optimal control of Volterra type stochastic difference equations

Many processes in automatic regulation, physics, etc. can be modelled by stochastic difference equations. One of the main problems of the theory of difference equations and their applications is connected with stability and optimal control [1]. In this paper we discuss the optimal control of second-kind Volterra type stochastic difference equations. In [2–9] for Volterra type stochastic integral equations, analogous results were obtained.     

Stability Properties of Cerebellar Neural Networks: The Purkinje Cell — Climbing Fiber Dynamic Module

In the last few decades it has been proven, that the cerebellum takes part in learning the bulk of motor control. The mechanisms which provide such properties are still largely unknown, but an involvement of parallel fibers and climbing fibers in this process, as have been proposed decades ago in cerebellar learning theories, is now clear. Among difficulties of the learning theories is an evident necessity for spontaneous activity of the cerebellar climbing fibers [5]. Recently, the group of M. Mauk proposed an elegant explanation of this inconsistency [11, 12]. We present here a stochastic model of a cerebellar module, based on this new approach. Theoretical treatment yields some consequences for experimental verification. Besides an explanation of real cerebellar functions, the analyzed control system presents a new paradigm for neural network memorizing systems.     

Stochastic adaptive control and prediction based on a modified least squares--The general delay-colored noise case

In [1], global convergence for a stochastic adaptive control based on modified least-squares algorithms has been established. However, the proof of Lemma 3.4 in [1] is questionable. A similar question existed in the proof ofdelta(t - d) rightarrow 0in [2]. Without using this conclusion, the present note attempts to establish global convergence for a discrete-time stochastic adaptive control and prediction based on slightly modified least-squares algorithms for linear time-invariant discrete-time systems having general delay and colored noise.     

On selecting a low-order model using the dominant mode concept

A technique for selecting a low-order system to approximate a high-order model has been suggested by Davison [2]. A critical component in this technique is the criterion used to select the most appropriate order and modes for the low-order approximation. Criteria have been discussed and analyzed by Mahapatra [5], [6], Rao, Lamba, and Rao [7], and Elrazaz and Sinha [3]. In this note we overcome deficiencies in the criteria that have been proposed and we introduce a new criterion which is rigorously justified. The criterion we suggest is also applicable when eigenvalues of the system are nonreal.     

基于自抗扰控制的随机扰动库存系统优化模型

针对随机扰动造成的企业库存系统缺货、库存水平增加和订货波动增大的问题,提出一种基于自抗扰控制（ADRC）的随机扰动库存系统优化模型。首先,根据进销存产品流和信息流的运营管理逻辑,通过拉普拉斯变换得到了库存系统的传递函数并将其转换成一类二阶状态空间标准式;然后,设计了一种包括跟踪微分器、扩张状态观测器和非线性状态误差反馈控制率的基于ADRC的随机扰动库存系统优化模型,从而在保证系统稳定的前提下,控制补偿随机扰动对库存系统的影响;最后,利用行业数据进行仿真实验,以验证ADRC优化模型对随机扰动库存系统优化的有效性。仿真实验结果表明,与无ADRC的库存反馈控制模型相比,基于ADRC的随机扰动库存系统优化模型可减少40%的库存剩余,减小47.4%的订货量均值,降低39.3%的订货量波动,并极大地改善随机扰动下企业库存系统的缺货现象。由此可见,基于ADRC的随机扰动库存系统优化模型能够指导企业合理订货,降低企业库存水平,从动态的角度提高库存系统的稳定性,为企业的实际生产运营提供科学的理论借鉴和应对方法。     

A note on the existence and uniqueness of mild solutions to neutral stochastic partial functional differential equations with non-Lipschitz coefficients

In this note, we study the existence and uniqueness of mild solutions to neutral stochastic partial functional differential equations under some Carathéodory-type conditions on the coefficients by means of the successive approximation. In particular, we generalize and improve the results that appeared in Govindan [T.E. Govindan, Almost sure exponential stability for stochastic neutral partial functional differential equations, Stochastics 77 (2005) 139–154] and Bao and Hou [J. Bao, Z. Hou, Existence of mild solutions to stochastic neutral partial functional differential equations with non-Lipschitz coefficients, Comput. Math. Appl. 59 (2010) 207–214].     

The improved stability analysis of the backward Euler method for neutral stochastic delay differential equations

The aim of this paper is to improve some results obtained in our earlier paper [Z. Yu and M. Liu, Almost surely asymptotic stability of numerical solutions for neutral stochastic delay differential equations, Discrete Dyn. Nat. Soc. 2011 (2011), article id 217672, 11 p., doi:10.1155/2011/217672]. In this paper, we establish an improved theorem and show that the backward Euler method can reproduce the property of almost sure and mean square exponential stability of exact solutions to neutral stochastic delay differential equations. To obtain the desired result, some new proof techniques are adopted.     

Choice of θ and its effects on stability in the stochastic θ-method of stochastic delay differential equations

The second author's work [F. Wu, X. Mao, and L. Szpruch, Almost sure exponential stability of numerical solutions for stochastic delay differential equations, Numer. Math. 115 (2010), pp. 681–697] and Mao's papers [D.J. Higham, X. Mao, and C. Yuan, Almost sure and moment exponential stability in the numerical simulation of stochastic differential equations, SIAM J. Numer. Anal. 45 (2007), pp. 592–607; X. Mao, Y. Shen, and G. Alison, Almost sure exponential stability of backward Euler–Maruyama discretizations for hybrid stochastic differential equations, J. Comput. Appl. Math. 235 (2011), pp. 1213–1226] showed that the backward Euler–Maruyama (BEM) method may reproduce the almost sure stability of stochastic differential equations (SDEs) without the linear growth condition of the drift coefficient and the counterexample shows that the Euler–Maruyama (EM) method cannot. Since the stochastic θ-method is more general than the BEM and EM methods, it is very interesting to examine the interval in which the stochastic θ-method can capture the stability of exact solutions of SDEs. Without the linear growth condition of the drift term, this paper concludes that the stochastic θ-method can capture the stability for θ∈(1/2, 1]. For θ∈[0, 1/2), a counterexample shows that the stochastic θ-method cannot reproduce the stability of the exact solution. Finally, two examples are given to illustrate our conclusions.     

Asymptotical stability of 2-D linear discrete stochastic systems

The main goal of the present paper is to find computable stability criteria for two-dimensional stochastic systems based on Kronecker product and nonnegative matrices theory. First, 2-D discrete stochastic system model is established by extending system matrices of the well-known Fornasini–Marchesini?s second model into stochastic matrices. The elements of these stochastic matrices are second-order, weakly stationary white-noise sequences. Second, a necessary and sufficient condition for 2-D stochastic systems is presented, this is the first time that has been proposed. Third, computable mean-square asymptotic stability criteria are derived via Kronecker product and the nonnegative matrix theory. The criteria are only sufficient conditions. Finally, illustrative examples are provided.     

How non-zero initial conditions affect the minimality of linear discrete-time systems

From the state-space approach to linear systems, promoted by Kalman, we learned that minimality is equivalent with reachability together with observability. Our past research on optimal reduced-order LQG controller synthesis revealed that if the initial conditions are non-zero, minimality is no longer equivalent with reachability together with observability. In the behavioural approach to linear systems promoted by Willems, that consider systems as exclusion laws, minimality is equivalent with observability. This article describes and explains in detail these apparently fundamental differences. Out of the discussion, the system properties weak reachability or excitability, and the dual property weak observability emerge. Weak reachability is weaker than reachability and becomes identical only if the initial conditions are empty or zero. Weak reachability together with observability is equivalent with minimality. Taking the behavioural systems point of view, minimality becomes equivalent with observability when the linear system is time invariant. This article also reveals the precise influence of a possibly stochastic initial state on the dimension of a minimal realisation. The issues raised in this article become especially apparent if linear time-varying systems (controllers) with time-varying dimensions are considered. Systems with time-varying dimensions play a major role in the realisation theory of computer algorithms. Moreover, they provide minimal realisations with smaller dimensions. Therefore, the results of this article are of practical importance for the minimal realisation of discrete-time (digital) controllers and computer algorithms with non-zero initial conditions. Theoretically, the results of this article generalise the minimality property to linear systems with time-varying dimensions and non-zero initial conditions.     

An integrated system design environment: Concepts and a status report

In the construction of requirements specifications for a given problem, it is generally recommended that overspecification of the problem solution be avoided [1]. Such overspecification tends to distort the functionality required by suggesting implementation concepts at the outset. In order to avoid overspecification, and to provide a support environment to the specifier, a four-stage system design environment is proposed and has been partially implemented over a three-year period. The theoretical basis of this approach is explained in [2]. Our system-level specification language (DODAN) is developed in [3]. Based on this specification language, a prototype (DAA) [4, 5, 6] for supporting the requirements specification stage has been implemented. Our other protype (DARMS) addressing the module specification stage was developed in [7, 8]. In this paper, the current status of the project is described with an emphasis on the requirements specification stage.     

n值乘积逻辑系统中的随机化研究

利用赋值集的随机化方法,在n值乘积逻辑中提出了公式的随机真度,证明了所有公式的随机真度之集在[0,1]中没有孤立点;给出了两公式间的D_πn-相似度与伪距离的概念,并建立了D_πn逻辑度量空间,证明了此空间没有孤立点。     

Comment on "On selecting a low-order model using the dominant mode concept"

In the above-mentioned paper [1], the authors presented a criterion for selecting the order of a low-order system to approximate a high-order model. Their criterion is very similar to what has been presented before in [2] and [3]. The authors claimed that the extension to handle systems with complex eigenvalues [3] is incorrect. Also, they used examples to show the superiority of their criterion. In this comment, it will be demonstrated that their claims are not absolutely correct.     

Exponential stability of discrete-time filters for bounded observation noise

This paper proves exponential asymptotic stability of discrete-time filters for the estimation of solutions to stochastic difference equations, when the observation noise is bounded. No assumption is made on the ergodicity of the signal. The proof uses the Hilbert projective metric, introduced into filter stability analysis by Atar and Zeitouni [1,2]. It is shown that when the signal noise is sufficiently regular, boundedness of the observation noise implies that the filter update operation is, on average, a strict contraction with respect to the Hilbert metric. Asymptotic stability then follows.     

A two-stage stochastic programming model for the parallel machine scheduling problem with machine capacity

This paper proposes a two-stage stochastic programming model for the parallel machine scheduling problem where the objective is to determine the machines' capacities that maximize the expected net profit of on-time jobs when the due dates are uncertain. The stochastic model decomposes the problem into two stages: The first (FS) determines the optimal capacities of the machines whereas the second (SS) computes an estimate of the expected profit of the on-time jobs for given machines' capacities. For a given sample of due dates, SS reduces to the deterministic parallel weighted number of on-time jobs problem which can be solved using the efficient branch and bound of M’Hallah and Bulfin [16]. FS is tackled using a sample average approximation (SAA) sampling approach which iteratively solves the problem for a number of random samples of due dates. SAA converges to the optimum in the expected sense as the sample size increases. In this implementation, SAA applies a ranking and selection procedure to obtain a good estimate of the expected profit with a reduced number of random samples. Extensive computational experiments show the efficacy of the stochastic model.