SMOOTHNESS OF INERTIAL MANIFOLD UNDER TIME DISCRETIZATION

In this paper we discuss the smoothness of inertial manifolds under time discretization. By the fibre contract principle, see Section 4, we obtain a sufficient condition for C-k(k greater than or equal to 1) inertial manifolds. In view of the numerical computation for dissipative nonlinear evolution equations, it is more important to consider the discretized case than continuous case([3]).

TIME DISCRETIZATION SCHEMES FOR AN INTEGRO-DIFFERENTIAL EQUATION OF PARABOLIC TYPE

In this paper a new approach for time discretization of an integro-differential equation of parabolic type is proposed. The methods are based on the backward-Euler and Crank-Nicolson Schemes but the memory and computational requirements are greatly reduced without assuming more regularities on the solution u.

HERMITE WENO SCHEMES WITH LAX-WENDROFF TYPE TIME DISCRETIZATIONS FOR HAMILTON-JACOBI EQUATIONS

In this paper, we use Hermite weighted essentially non-oscillatory （HWENO） schemes with a Lax-Wendroff time discretization procedure, termed HWENO-LW schemes, to solve Hamilton-Jacobi equations. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both the function and its first derivative values are evolved in time and are used in the reconstruction. One major advantage of HWENO schemes is its compactness in the reconstruction. We explore the possibility in avoiding the nonlinear weights for part of the procedure, hence reducing the cost but still maintaining non-oscillatory properties for problems with strong discontinuous derivative. As a result, comparing with HWENO with Runge-Kutta time discretizations schemes （HWENO-RK） of Qiu and Shu [19] for Hamilton-Jacobi equations, the major advantages of HWENO-LW schemes are their saving of computational cost and their compactness in the reconstruction. Extensive numerical experiments are performed to illustrate the capability of the method.

Local discontinuous Galerkin methods with explicit-implicit-null time discretizations for solving nonlinear diffusion problems

In this paper,we discuss the local discontinuous Galerkin methods coupled with two specific explicitimplicit-null time discretizations for solving one-dimensional nonlinear diffusion problems Ut=(a(U)Ux)x.The basic idea is to add and subtract two equal terms a0 Uxx the right-hand side of the partial differential equation,then to treat the term a0 Uxx implicitly and the other terms(a(U)Ux)x-a0 Uxx explicitly.We give stability analysis for the method on a simplified model by the aid of energy analysis,which gives a guidance for the choice of a0,i.e.,a0≥max{a(u)}/2 to ensure the unconditional stability of the first order and second order schemes.The optimal error estimate is also derived for the simplified model,and numerical experiments are given to demonstrate the stability,accuracy and performance of the schemes for nonlinear diffusion equations.

STRONG STABILITY PRESERVING PROPERTY OF THE DEFERRED CORRECTION TIME DISCRETIZATION

In this paper, we study the strong stability preserving （SSP） property of a class of deferred correction time discretization methods, for solving the method-of-lines schemes approximating hyperbolic partial differential equations.

TWO-STAGE FOURTH-ORDER ACCURATE TIME DISCRETIZATIONS FOR 1D AND 2D SPECIAL RELATIVISTIC HYDRODYNAMICS

This paper studies the two-stage fourth-order accurate time discretization[J.Q.Li and Z.F.Du,SIAM J.Sci.Comput.,38(2016)]and its application to the special relativistic hydrodynamical equations.Our analysis reveals that the new two-stage fourth-order accurate time discretizations can be proposed.With the aid of the direct Eulerian GRP(generalized Riemann problem)methods and the analytical resolution of the local“quasi 1D”GRP,the two-stage fourth-order accurate time discretizations are successfully implemented for the 1D and 2D special relativistic hydrodynamical equations.Several numerical experiments demonstrate the performance and accuracy as well as robustness of our schemes.

ERROR ESTIMATES FOR THE TIME DISCRETIZATION FOR NONLINEAR MAXWELL'S EQUATIONS

This paper is devoted to the study of a nonlinear evolution eddy current model of the type δtB（H） ＋ △↓× （ △↓ × H） =0 subject to homogeneous Dirichlet boundary conditions H × v = 0 and a given initial datum. Here, the magnetic properties of a soft ferromagnet are linked by a nonlinear material law described by B（H）. We apply the backward Euler method for the time discretization and we derive the error estimates in suitable function spaces. The results depend on the nonlinearity of B（H）.

Simulations of Shallow Water Equations by Finite Difference WENO Schemes with Multilevel Time Discretization

In this paper we study a class of multilevel high order time discretization procedures for the finite difference weighted essential non-oscillatory(WENO)schemes to solve the one-dimensional and two-dimensional shallow water equations with source terms.Multilevel time discretization methods can make full use of computed information by WENO spatial discretization and save CPU cost by holding the former computational values.Extensive simulations are performed,which indicate that,the finite difference WENO schemes with multilevel time discretization can achieve higher accuracy,and are more cost effective than WENO scheme with Runge-Kutta time discretization,while still maintaining nonoscillatory properties.

The Uniform L^2 Behavior for Time Discretization of an Evolution Equation

The uniform L^2 stability and convergence properties for the time discretization of an evolution equation with a memory term are studied. The methods are based on the second-order backward difference methods. The memory term is approximated by the second-order convolution quadrature and interpolant quadrature.

The MAP/PH(PH/PH)/1 Discrete-time Queuing System with Repairable Server

In this paper, we discuss a discrete time repairable queuing system with Markovian arrival process, where lifetime of server, service time and repair time of server are all discrete phase type random variables. Using the theory of matrix geometric solution, we give the steady state distribution of queue length and waiting time. In addition, the stable availability of the system is also provided.

A Discrete-Time Stochastic Traffic Assignment Model

A discrete time stochastic traffic assignment model is proposed. The model provides a discrete time description of the variations of flows on a road network during a day or a peak period. The congestion effect at links and link junctions are taken into account. The first in first out principle is enforced on all links at all periods of the day. A stochastic user equilibrium assignment is achieved when the tripmaker is unable to find better travel alternatives. A computational procedure is also presented.

NECESSARY AND SUFFICIENT CONDITIONS FOR QUADRATIC STABILITY OF UNCERTAIN DISCRETE TIME SYSTEMS

The robust stability analysis of discrete time systems with fast time varying uncertainties is considered in this paper. The necessary and sufficient conditions for quadratic stability are presented. Moreover, the stability robustness index is introduced as the measurement of the stability robustness. For the systems with given uncertain parameter bounds, checking the necessary and sufficient conditions and calculating the stability robust index are converted to solving minimax problems. It is shown that the maximization can be reduced to comparisons between the functional values of the corners when the parameter region is bounded by hyperpolydredon, and any local minimum value in the minimization is exactly the global minimum.

Intrusion Detection System for PS-Poll DoS Attack in 802.11 Networks Using Real Time Discrete Event System

Wi-Fi devices have limited battery life because of which conserving battery life is imperative. The 802.11 Wi-Fi standard provides power management feature that allows stations(STAs) to enter into sleep state to preserve energy without any frame losses. After the STA wakes up, it sends a null data or PS-Poll frame to retrieve frame(s) buffered by the access point(AP), if any during its sleep period. An attacker can launch a power save denial of service(PS-DoS) attack on the sleeping STA(s) by transmitting a spoofed null data or PS-Poll frame(s) to retrieve the buffered frame(s) of the sleeping STA(s) from the AP causing frame losses for the targeted STA(s). Current approaches to prevent or detect the PS-DoS attack require encryption,change in protocol or installation of proprietary hardware. These solutions suffer from expensive setup, maintenance, scalability and deployment issues. The PS-DoS attack does not differ in semantics or statistics under normal and attack circumstances.So signature and anomaly based intrusion detection system(IDS) are unfit to detect the PS-DoS attack. In this paper we propose a timed IDS based on real time discrete event system(RTDES) for detecting PS-DoS attack. The proposed DES based IDS overcomes the drawbacks of existing systems and detects the PS-DoS attack with high accuracy and detection rate. The correctness of the RTDES based IDS is proved by experimenting all possible attack scenarios.

Iterative Learning Control for Discrete-time Stochastic Systems with Quantized Information

An iterative learning control (ILC) algorithm using quantized error information is given in this paper for both linear and nonlinear discrete-time systems with stochastic noises. A logarithmic quantizer is used to guarantee an adaptive improvement in tracking performance. A decreasing learning gain is introduced into the algorithm to suppress the effects of stochastic noises and quantization errors. The input sequence is proved to converge strictly to the optimal input under the given index. Illustrative simulations are given to verify the theoretical analysis. © 2014 Chinese Association of Automation.

Discrete time transfer matrix method for dynamics of multibody system with flexible beams moving in space

In this paper, by defining new state vectors and developing new transfer matrices of various elements mov- ing in space, the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to study the dynamics of multibody system with flexible beams moving in space. Formulations and numerical example of a rigid- flexible-body three pendulums system moving in space are given to validate the method. Using the new method to study the dynamics of multi-rigid-flexible-body system mov- ing in space, the global dynamics equations of system are not needed, the orders of involved matrices of the system are very low and the computational speed is high, irrespec- tive of the size of the system. The new method is simple, straightforward, practical, and provides a powerful tool for multi-rigid-flexible-body system dynamics.

Real-time crash prediction on freeways using data mining and emerging techniques

Recent advances in intelligent transportation system allow traffic safety studies to extend from historic data-based analyses to real-time applications. The study presents a new method to predict crash likelihood with traffic data collected by discrete loop detectors as well as the web-crawl weather data. Matched case-control method and support vector machines （SVMs） technique were employed to identify the risk status. The adaptive synthetic over-sampling technique was applied to solve the imbalanced dataset issues. Random forest technique was applied to select the contributing factors and avoid the over-fitting issues. The results indicate that the SVMs classifier could successfully classify 76.32% of the crashes on the test dataset and 87.52% of the crashes on the overall dataset, which were relatively satisfactory compared with the results of the previous studies. Compared with the SVMs classifier without the data, the SVMs classifier with the web-crawl weather data increased the crash prediction accuracy by 1.32% and decreased the false alarm rate by 1.72%, showing the potential value of the massive web weather data. Mean impact value method was employed to evaluate the variable effects, and the results are identical with the results of most of previous studies. The emerging technique based on the discrete traffic data and web weather data proves to be more applicable on real- time safety management on freeways.

H_∞ State Feedback Delay-dependent Control for Discrete Systems with Multi-time-delay

In this paper, H ∞ state feedback control with delay information for discrete systems with multi-time-delay is discussed. Making use of linear matrix inequality (LMI) approach, a time-delay-dependent criterion for a discrete system with multi-time-delay to satisfy H ∞ performance indices is induced, and then a strategy for H ∞ state feedback control with delay values for plant with multi-time-delay is obtained. By solving corresponding LMI, a delay-dependent state feedback controller satisfying H ∞ performance indices is designed. Finally, a simulation example demonstrates the validity of the proposed approach. Keywords Multi-time-delay - discrete time system - LMI - delay-dependent - H ∞ control Bai-Da Qu received B. S. degree in electrical automation from Fuxin Mining Institute, China in 1982, M. Eng. degree from Hefei University of Polytechnology in 1990, and Ph.D from Northerneastern University in 1999. He was an electro-mechanical engineer at Erdaohezi Mine, Heilongjiang, China from 1982 to 1990, a Lecturer, Senior Engineer, Associate Professor and Professor in Shenyang Institue of Technology from 1990 to 2002. He is currently a professor in Communication and Control Engineering School, Southern Yangtze University. His research interests include control theory and applications (robust control, H ∞ control, time-delay systems, complex systems), system engineering (modeling, analysis and simulation, MIS,CMIS), power-electronics and electrical driving, signal detecting and process, industrial automation.

H_∞ controller synthesis of piecewise discrete time linear systems

This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ performance and the controller can be obtained by solving a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapunov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.

Digitalization of mine operations:Scenarios to benefit in real-time truck dispatching

One of the key factors in a profitable open-pit mine is the efficiency of the waste disposal system. Using GPS-technology, the truck-dispatching decisions can be made in real-time but the chosen strategy has a crucial role. Therefore, finding the optimal dispatching strategy for truck-shovel operations is extremely important. Dispatching strategies have been reported in the literature, but the comparison of these strategies is still missing. This paper illustrates the differences between the strategies by conducting a stochastic simulation study based on the data gathered from an actual mine. The findings underline the importance of the global vision in dispatching decisions.

Asymptotic controllability of a class of discrete-time systems with disturbances

This article deals with the uniformly globally asymptotic controllability of discrete nonlinear systems with disturbances.It is shown that the system is uniformly globally asymptotic controllability with respect to a closed set if and only if there exists a smooth control Lyapunov function.Further, it is obtained that the control Lyapunov function may be used to construct a feedback law to stabilize the closed-loop system.In addition, it is proved that for periodic discrete systems, the resulted control Lyapunov functions are also time periodic.