Collocation and finite difference-collocation methods for the solution of nonlinear Klein-Gordon equation

Two numerical techniques based on the finite difference and collocation methods are presented for the solution of nonlinear Klein-Gordon equation. The operational matrix of derivative for the cubic B-spline scaling functions is presented and is utilized to reduce the solution of nonlinear Klein-Gordon equation to the solution of algebraic equations. Illustrative examples are included to demonstrate the validity and applicability of the new techniques.     

Practical frequency response analysis of non-linear time-delayed differential or difference equation models

A systematic algorithm for generating the polyharmonic balance equations for any system within a broad class of time-delayed differential, or non-linear difference equation models, is presented. The method, which is readily automated, enables the balance equations to be written down directly in terms of the coefficients of the governing equation, and the complex amplitudes of a general harmonic waveform. The system frequency response or amplitude dependent describing function is then readily computed. The method is illustrated by means of examples including both a time-delayed differential system example and a discrete time NARX model application. The results are validated against detailed numeric simulation which confirms the accuracy and efficacy of the approach.     

Reduced order controller design for discrete time systems

Robust discrete control system design techniques and model reduction are discussed. A new linear quadratic guussian/loop transfer recovery procedure for discrete time systems is presented. In this technique, a full-state feedback or an output injection feedback is designed which has the desired loop shape, and then recovered by a realizable linear quadratic gaussian controller. To do this, results that show the effects of the weighting matrices (noise intensities) on linear quadratic regulator (Kalman-Bucy filter) return difference and inverse-return difference arc derived and a procedure to recover the linear quadratic regulator loop transfer function is described. The complexity of the resulting controller is then reduced without causing closed-loop instability. Two methods for model reduction are considered. The first is the discrete balanced realization and the second is P frequency weighting technique where it is possible to vary the approximation accuracy with frequency. The controller design and reduction techniques are illustrated by designing a reduced order controller for an 8th order lumped inertia flexible mechanical system.     

Intra-Period (Within-Day) Dynamic Models for Continuous Services

To simulate important aspect of some transportation systems (e.g. demand peaks, temporary capacity variations, temporary over-saturation of supply elements, and formation and dispersion of queues) a new class of models, referred to in the literature as Dynamic Traffic Assignment (DTA) models, have been recently developed. Although Dynamic Traffic Assignment to networks is a relatively new research subject, a great number of models have been proposed in the last two decades. These can be divided in two main classes according to the typology of service they aim at simulating. These are continuous services, considering transportation services available at any time and accessible from several points, such as the services offered by individual road modes (car, bicycle etc.), and scheduled services simulating services available only at certain times and that can be accessed only at certain locations (terminals, stations, airports etc.). In this paper the focus is on continuous services. Models proposed in the literature are reviewed and classified according to basic assumptions on the flow structure, i.e. whether a continuous or a discrete approach is followed, and on the representation of time (discrete vs. continuous). A general modeling framework consisting of supply, demand, and demand-supply interaction models, and including most of the existing specifications is presented both for the discrete time-discrete flow and continuous time continuous flow cases.     

摄动离散矩阵Lyapunov方程解的估计

研究摄动离散矩阵Lyapunov方程解的估计问题,利用矩阵运算性质及Lyapunov稳定性理论,给出在结构不确定性假设下方程解的存在条件及解的上下界估计,估计结果由一个线性矩阵不等式(LMI)和两个矩阵代数Riccati方程确定．针对几种不确定性假设,进一步给出矩阵代数Riccati方程的具体形式．最后通过一个算例说明了所得结果的有效性．     

Recursive output error identification algorithms theory and evaluation

Several recurisve algorithms for parametric identification of discrete time systems derived from Model Reference Adaptive System (M.R.A.S.) techniques are analysed. All these algorithms belong to the class of output error methods which have been very little discussed previously in the identification literature. These algorithms are analysed in the deterministic and stochastic environment using the Equivalent Feedback Representation (E.F.R.) and Ordinary Differential Equation (O.D.E.) methods respectively. A comparative evaluation of these algorithms is presented. This comparison is made also with respect to various widely used recursive algorithms belonging to the ‘equation error method’ (extended least squares, approximate maximum likelihood).     

Numerical solutions of the one-phase classical Stefan problem using an enthalpy green element formulation

The enthalpy method is exploited in tackling a heat transfer problem involving a change of state. The resulting governing equation is then solved with a hybrid finite element - boundary element technique known as the Green element method (GEM). Two methods of approximation are employed to handle the time derivative contained in the discrete element equation. The first involves a finite difference method, while the second utilizes a Galerkin finite element approach. The performance of both methods are assessed with a known closed form solution. The finite element based time discretization, despite its greater challenge, yields less reliable numerical results. In addition a numerical stability test of both methods based on a Fourier series analysis explain the dispersive characters of both techniques, and confirms that replication of correct results is largely attributed to their ability to handle the harmonics of small wavelengths which are usually dominant in the vicinity of a front.     

Rationalization of singularly perturbed continuous systems with time delays

The state equation of a continuous time system with time delay is nonlinear. Therefore, its transfer function is irrational, which is difficult to solve. However, the transfer function of a discrete time state equation with time delay is rational. Hence, the problem can be solved easily. A rationalization of the singularly perturbed continuous system of single and multiple time delays is presented by setting a delay coefficient. The technique is a powerful tool when solving the singularly perturbed continuous equation with single and multiple time delays instead of when using numerical methods such as the Runge-Kutta algorithm.     

自行火炮系统作战效能建模与仿真研究

在综合研究国内外效能评估理论和方法的基础上,根据多年来自行火炮发展建设和作战运用的实际需求,建立了对抗条件下战斗、保障、指挥控制等分系统的作战效能及作战系统评估模型。依据可靠性、维修性数字仿真的基本理论,利用Monte—Carlo方法对某型自行火炮战场对抗阶段进行仿真,可以实现自行火炮可靠性、维修性及系统作战效能的动态评估。该方法受评估者的主观性影响较小,为系统效能的动态评估系统的设计构想提出了评估思路。该模型可以为自行火炮系统的方案论证、工程研制、鉴定定型和作战运用等提供决策依据。     

The factorization of discrete-process spectral matrices

A technique is presented for salving the discrete version of the multidimensional Wiener-Hopf equation by spectral factorization. This equation is derived to establish a need for spectral factorization and to determine the requirements of the factors of the spectral matrix. The method of factoring the spectral matrix of continuous systems, developed by Davis, is then extended to discrete systems. More specifically, a matrixH(z)must be found such that the matrix of the spectra of the input signals equals the product ofH(z^{-1})andH^{T}(z). A technique for finding this matrix is presented. The nonanticipatoriness as well as the stability of the elements ofH(z)andH^{-1}(z)must be and is guaranteed. It is then shown that the solution to the discrete Wiener-Hopf equation is unique.     

SYSTEM THEORETIC FORMALISMS FOR COMBINED DISCRETE-CONTINUOUS SYSTEM SIMULATION

In this paper we present an approach to combined discrete-continuous modelling which can be used to model and simulate an intelligent multi-layer control architecture as can be found in high autonomy systems. The modelling approach is based on system theoretical concepts; the three system specification formalisms-differential equation, discrete time, and the discrete event system specification formalism-have been combined to facilitate multi-formalisms modelling. Simulation concepts are based on the abstract simulator concept for discrete event simulation developed by Zeigler. Similar simulation methods have been developed to simulate modular, hierarchical discrete time and differential equation specified systems as well as multi-formalism models. Included in the paper are several examples of multi-formalism models together with the simulation results from the STIMS environment-an implementation of the modelling and simulation concepts in Interlisp-D/LOOPS.     

Bounds on buffer overflow probabilities in communication systems

A model to analyze the buffer behaviour in a multiplexor is derived, based on the analogy between the buffer occupancy in a discrete time model of multiplexing and the waiting time of a GI/G/1 queueing system.The bounding techniques developed earlier by Kingman and Ross are extended to the discrete time model. Simple and useful bounds are obtained for the buffer overflow probabilities under general assumptions concerning incoming message traffic characteristics. Numerical examples are presented and compared with other methods.     

A stable residue method for model reduction of discrete systems

A new combined method for model reduction of a discrete system in Z-transfer function is presented. Conventional stable methods such as dominant poles retention, Routh approximation and stability equation method, are used to reduce the order of denominator polynomial of the original model. Residue method is used to determine the coefficients of the numerator polynomial of the reduced model such that the sum of the square errors between the unit step responses of the reduced and original models is a minimum. The advantages of the new method are that it does not require evaluating the time responses, and the reduced model is always stable provided the original model is stable. Furthermore, both the time and frequency domain characteristics of the original model can be preserved in the reduced model.     

Typical examples of using the atoment language

Atoment is a domain-specific language of executable specifications applied to describe methods and techniques of program verification. In this paper, a series of typical examples of using the Atoment language covering program models; the operational, transformational, and axiomatic semantics; and the formal specification of programming languages is presented.     

A high-order compact finite difference method and its extrapolation for fractional mobile/immobile convection–diffusion equations

This paper is concerned with high-order numerical methods for a class of fractional mobile/immobile convection–diffusion equations. The convection coefficient of the equation may be spatially variable. In order to overcome the difficulty caused by variable coefficient problems, we first transform the original equation into a special and equivalent form, which is then discretized by a fourth-order compact finite difference approximation for the spatial derivative and a second-order difference approximation for the time first derivative and the Caputo time fractional derivative. The local truncation error and the solvability of the resulting scheme are discussed in detail. The (almost) unconditional stability and convergence of the method are proved using a discrete energy analysis method. A Richardson extrapolation algorithm is presented to enhance the temporal accuracy of the computed solution from the second-order to the third-order. Applications using two model problems give numerical results that demonstrate the accuracy of the new method and the high efficiency of the Richardson extrapolation algorithm.     

A review of soft computing applications in supply chain management

It is broadly recognised by global companies that supply chain management is one of the major core competencies for an organisation to compete in the marketplace. Organisational strategies are mainly concentrated on improvement of customer service levels as well as reduction of operational costs in order to maintain profit margins. Therefore supply chain performance has attracted researchers’ attention. A variety of soft computing techniques including fuzzy logic and genetic algorithms have been employed to improve effectiveness and efficiency in various aspects of supply chain management. Meanwhile, an increasing number of papers have been published to address related issues. The aim of this paper is to summarise the findings by a systematic review of existing research papers concerning the application of soft computing techniques to supply chain management. Some areas in supply chain management that have rarely been exposed in existing papers, such as customer relationship management and reverse logistics, are therefore suggested for future research.     

Numerical solution of Riccati equation using the cubic B-spline scaling functions and Chebyshev cardinal functions

Two numerical techniques are presented for solving the solution of Riccati differential equation. These methods use the cubic B-spline scaling functions and Chebyshev cardinal functions. The methods consist of expanding the required approximate solution as the elements of cubic B-spline scaling function or Chebyshev cardinal functions. Using the operational matrix of derivative, we reduce the problem to a set of algebraic equations. Some numerical examples are included to demonstrate the validity and applicability of the new techniques. The methods are easy to implement and produce very accurate results.     

工作流过程建模中的形式化验证技术

工作流过程建模是一个复杂且易错的过程．若过程定义在投入运行之后被发现有错,则修复错误的代价相当高,这个问题引起了研究界和工业界的高度重视．因此,在建模阶段进行有效的过程验证是十分必要的．综述了工作流过程验证技术的发展现状,包括强调验证的重要性,叙述了需要验证的问题和复杂度;介绍了对验证方法的要求;讨论了过程合理性验证和化简验证技术等;并通过对研究现状的分析和对比,提出了仍然没有解决的问题和将来的工作．     

Estimating Bayes factors via thermodynamic integration and population MCMC

A Bayesian approach to model comparison based on the integrated or marginal likelihood is considered, and applications to linear regression models and nonlinear ordinary differential equation (ODE) models are used as the setting in which to elucidate and further develop existing statistical methodology. The focus is on two methods of marginal likelihood estimation. First, a statistical failure of the widely employed Posterior Harmonic Mean estimator is highlighted. It is demonstrated that there is a systematic bias capable of significantly skewing Bayes factor estimates, which has not previously been highlighted in the literature. Second, a detailed study of the recently proposed Thermodynamic Integral estimator is presented, which characterises the error associated with its discrete form. An experimental study using analytically tractable linear regression models highlights substantial differences with recently published results regarding optimal discretisation. Finally, with the insights gained, it is demonstrated how Population MCMC and thermodynamic integration methods may be elegantly combined to estimate Bayes factors accurately enough to discriminate between nonlinear models based on systems of ODEs, which has important application in describing the behaviour of complex processes arising in a wide variety of research areas, such as Systems Biology, Computational Ecology and Chemical Engineering.     

加热炉网络控制系统的最少拍响应控制策略

研究加热炉网络控制系统的最少拍响应控制策略。推导了加热炉网络控制系统的频域和离散型状态方程的数学模型,并采用时间戳神经网络,对不确定、时变的网络信息传输延时进行预测。重点研究了具有最少拍响应的数字控制器设计方法,导出了数字控制器控制算法。仿真结果表明,提出的控制算法实现了加热炉精确的温度控制,无稳态偏差,并具有良好的动、静态特性。