An implicit MacCormack scheme for unsteady flow calculations

This paper describes the implicit MacCormack scheme [1] in finite volume formulation. Unsteady flows with moving boundaries are considered using arbitrary Lagrangian–Eulerian approach.The scheme is unconditionally stable and does not require solution of large systems of linear equations. Moreover, the upgrade from explicit MacCormack scheme to implicit one is very simple and straightforward.Several computational results for 2D and 3D flows over profiles and wings are presented for the case of inviscid and viscous flows.     

A generic lazy evaluation scheme for exact geometric computations

We present a generic C++ design to perform exact geometric computations efficiently using lazy evaluations. Exact geometric computations are critical for the robustness of geometric algorithms. Their efficiency is also important for many applications, hence the need for delaying the costly exact computations at run time until they are actually needed, if at all. Our approach is generic and extensible in the sense that it is possible to make it a library that users can apply to their own geometric objects and primitives. It involves techniques such as generic functor-adaptors, static and dynamic polymorphism, reference counting for the management of directed acyclic graphs, and exception handling for triggering exact computations when needed. It also relies on multi-precision arithmetic as well as interval arithmetic. We apply our approach to the whole geometry kernel of Cgal.     

一种精确缩略图保持的图像加密方案

手机电脑平板等的普及,使得照片在日常生活中更容易获得,并且人们习惯将大量照片存储在云端。但是,在享受云存储带来的便利的同时,用户也容易受到隐私泄露的威胁。虽然学者们设计出许多图像加密方案用来防止隐私泄露,然而往往忽略了图像的可用性。最近,Tajik等人提出了一种精确缩略图保持的加密方案,能够很好地平衡图像的隐私与可用性。但是,该方案在加密过程中仅以2个像素为一组,效率较低。为此提出一种利用分割法加密图像的方案,该方案以3个像素为一组进行加密,用于保持密文图像的缩略图与明文图像的缩略图一致,并且该方案相比Tajik方案具有更高的效率。实验表明,这个方案能够使密文图像精确地保持与明文相同的缩略图,平衡了隐私和可用性。     

Multi-dimensional semi-Lagrangian scheme that guarantees exact conservation

A new numerical method that guarantees exact mass conservation is proposed to solve multi-dimensional hyperbolic equations in semi-Lagrangian form without directional splitting. The method is based on a concept of CIP scheme and keep the many good characteristics of the original CIP scheme. The CIP strategy is applied to the integral form of variable. Although the advection and non-advection terms are separately treated, the mass conservation is kept in a form of spatial profile inside a grid cell. Therefore, it retains various advantages of the semi-Lagrangian schemes with exact conservation that has been beyond the capability of conventional semi-Lagrangian schemes.     

Design for stability region maximization

The purpose of this correspondence is to apply to systems of the Lur'e type a design technique for maximizing the extent of the region of asymptotic stability. A specific example is given.     

An exact stability analysis test for single-parameter polynomially-dependent linear systems

We provide a new condition for testing the stability of a single-parameter, polynomially-dependent linear system of polynomial degree N of the form x/spl dot/=A(/spl rho/)x, A(/spl rho/)=/spl Sigma//sub i=0//sup N//spl rho//sup i/ A/sub i/ (1) over a compact interval. The test is nonconservative and can be cast as a convex feasibility problem in terms of a pair of linear matrix inequalities (LMIs).     

An enumeration scheme to generate constrained exact checkerboard patterns

Checkerboard patterns belong to a special class of 2-stage guillotine patterns that require less machine time to be cut. In this paper we propose an enumerative algorithm to generate exact constrained checkerboard patterns. At each node of the enumeration tree a constructive procedure is used to generate a feasible pattern. In addition, an upper bound on the objective function value is calculated to decide whether further branching from the node is worth. The algorithm was implemented and computational tests were performed. The test results indicate that the proposed scheme outperforms previous methods of the literature in terms of execution times.     

A novel numerical method for exact model matching problem with stability

In system design the exact model matching problem with stability consists of compensating a given system, using a realizable control law of a specified structure, in order to ensure the stability of the compensated system and achieve a target closed-loop transfer function. In this paper we develop a novel numerical method to verify the solvability of the problem for left invertible systems and further construct a desired solution. Our method has a complexity which is cubic in the state dimension of the system and the desired model and can be implemented in a numerically reliable way.     

Lyapunov-based exact stability analysis and synthesis for linear single-parameter dependent systems

We propose a class of polynomially parameter-dependent quadratic (PPDQ) Lyapunov functions for assessing the stability of single-parameter-dependent linear, time-invariant, (s-PDLTI) systems in a non-conservative manner. It is shown that the stability of s-PDLTI systems is equivalent to the existence of a PPDQ Lyapunov function. A bound on the degree of the polynomial dependence of the Lyapunov function in the system parameter is given explicitly. The resulting stability conditions are expressed in terms of a set of matrix inequalities whose feasibility over a compact and connected set can be cast as a convex, finite-dimensional optimisation problem. Extensions of the approach to state-feedback controller synthesis are also provided.     

An exact quadratic stability condition of uncertain linear systems

It is pointed out that in order to check the quadratic stability of a family of linear systems with a stable nominal system, the positive definiteness constraint can be dropped from the quadratic Lyapunov function     

An exact method for the stability analysis of time-delayed lineartime-invariant (LTI) systems

A general class of linear time invariant systems with time delay is studied. Recently, they attracted considerable interest in the systems and control community. The complexity arises due to the exponential type transcendental terms in their characteristic equation. The transcendentality brings infinitely many characteristic roots, which are cumbersome to elaborate as evident from the literature. A number of methodologies have been suggested with limited ability to assess the stability in the parametric domain of time delay. This study offers an exact, structured and robust methodology to bring a closure to the question at hand. Ultimately we present a unique explicit analytical expression in terms of the system parameters which not only reveals the stability regions (pockets) in the domain of time delay, but it also declares the number of unstable characteristic roots at any given pocket. The method starts with the determination of all possible purely imaginary (resonant) characteristic roots for any positive time delay. To achieve this a simplifying substitution is used for the transcendental terms in the characteristic equation. It is proven that the number of such resonant roots for a given dynamics is finite. Each one of these roots is created by infinitely many time delays, which are periodically distributed. An interesting property is also claimed next, that the root crossing directions at these locations are invariant with respect to the delay and dependent only on the crossing frequency. These two unique findings facilitate a simple and practical stability method, which is the highlight of the work     

Parametrization method for calculating exact stability bounds of stochastic linear systems with multiplicative noise

For deterministic time-invariant linear systems, stability results are quite simple. For stochastic systems, however, even for linear ones, they are rather complicated. In this paper, some results on second mean stability (mean square stability) of time-invariant linear systems with multiplicative noise are summarized and the parametrization method of getting an exact bound for pth mean stability (p ≥ 2) via second mean stability is stated. Moreover, relations between pth mean stabilities for various values of p are given. On the basis of these relations, a simpler method for getting sufficient conditions for pth mean stability is also given, though the resulting sufficient bound is, of course, more conservative. Comparative studies of various conditions are made by using examples.     

Modified quadratic loss function for a trivariate response with the exact feasible region for parameters

This paper deals with modification of Taguchi's quadratic quality loss function (QQLF) for a trivariate responses, each having a NtB (nominal-the-best) type quality characteristic and correlated in pairs. It tends to improve and extend results obtained in 0025 and 0035. Impossibility to solve nonlinear constraint in [6] resulted in an approximate algorithm to determine unknown parameters of QQLF. Here the nonlinear constraint is solved analytically and consequently the exact feasible region is obtained. The QQLF is formed by means of the parameters from the restrictive feasible region and proved suitable for all the types of correlation among quality characteristics.     

干支线混合区域的协调控制方案

为解决传统区域协调控制方案因算法复杂、输入量多、非实时性导致协调效果不佳的问题,提出一套以干线为主的区域协调控制方案.首先将区域预设为若干个子区并基于周期原则动态地对子区进行合并与拆分,然后在子区内部对干线采用绿波协调控制算法,获得子区最佳周期和各交叉口最佳相位差,最后对所有交叉口采用基于饱和度估计的单点绿信比优化算法,选择出下一周期最佳绿信比方案.与传统区域协调控制方案相比,该方案计算的复杂度降低、需要的输入量变少、能实时动态地对区域进行协调控制、协调效果更好.通过算例分析和系统仿真,使用该方案后,子区内部能获得大于30％的绿波带宽度,单个交叉口的平均停车次数比传统方案减少65％.     

An approach for computing the exact stability domain for a class of LTI parameter dependent systems

In this paper, the complete stability domain for both single- and multi-parameter dependent LTI systems is synthesized by extending existing results in the literature. This domain is calculated through a guardian map which involves the determinant of the Kronecker sum of a matrix with itself. The single parameter case is easily computable, whereas the multi-parameter case is more involved. The determinant of the bialternate sum of a matrix with itself is also exploited to reduce the computational complexity of the results presented in this paper.     

A simple procedure for the exact stability robustness computation of polynomials with affine coefficient perturbations

This paper considers the problem of the stability robustness computation of polynomials with coefficients which are affine functions of the parameter perturbations. A polynomial is said to be stable if its roots are contained in an arbitrarily pre-specified open set in the complex plane, and its stability robustness is then measured by the norm of the smallest parameter perturbation which destabilizes the polynomial. A simple and numerically effective procedure, which is based on the Hahn-Banach theorem of convex analysis and which is applicable for any arbitrary norm, is obtained to compute the stability robustness. The computation is then further simplified for the case when the norm used is the Hölder ∞-norm, 2-norm or 1-norm.     

实现比率遥操作系统稳定性与性能折衷的策略

临场感比率遥操作系统要求在保证系统稳定的同时能增强系统性能.本文通过系统建模、引入二端口网络的莱威林(Llewellyn)绝对稳定性准则,在定义比率系统的理想性能、导出实现理想性能的主从系统控制参数的约束条件后,分析了实现理想性能时系统的稳定性;基于莱威林准则,在实现理想性能的基础上调节主从系统阻抗,提出了在操作者与环境无源条件下能在系统绝对稳定性和增强性能之间折衷的控制策略.仿真表明了此策略的有效性.     

Global stability analysis scheme for a class of nonlinear time delay systems

We consider a class of nonlinear time delay systems created by generalizing the model for FAST TCP, an Internet congestion control algorithm. We achieve a time delay independent sufficient condition for the global asymptotic stability of the class of systems. The sufficient condition is verified by constructing two sequences that represent the lower and upper bound variations of the system trajectory in time, and showing that the two sequences converge to the equilibrium point of the system. The simulation results exemplify that the sufficient condition is valid for global asymptotic stability, and that the sufficient condition is a close approximation to the unknown necessary and sufficient condition for global asymptotic stability.     

An algorithm for the strip packing problem using collision free region and exact fitting placement

The irregular shape packing problem is approached. The container has a fixed width and an open dimension to be minimized. The proposed algorithm constructively creates the solution using an ordered list of items and a placement heuristic. Simulated annealing is the adopted metaheuristic to solve the optimization problem. A two-level algorithm is used to minimize the open dimension of the container. To ensure feasible layouts, the concept of collision free region is used. A collision free region represents all possible translations for an item to be placed and may be degenerated. For a moving item, the proposed placement heuristic detects the presence of exact fits (when the item is fully constrained by its surroundings) and exact slides (when the item position is constrained in all but one direction). The relevance of these positions is analyzed and a new placement heuristic is proposed. Computational comparisons on benchmark problems show that the proposed algorithm generated highly competitive solutions. Moreover, our algorithm updated some best known results.     

MacCormack方法优化烟雾模拟中Navier-Stokes方程对流项的求解

烟雾作为大规模虚拟战场和复杂环境仿真中的重要组成部分,对其进行模拟具有重要的意义.针对基于物理方法烟雾模拟中Navier-Stokes方程求解复杂、影响实时性的问题,提出用MacCormack求解Navier-Stokes方程对流项的方法.首先利用前向对流算子求解前向烟雾速度,然后利用后向对流算子求解后向烟雾速度,最后通过误差评估来修正已经计算的前向对流速度,得到下一时刻的烟雾速度.该方法简化了进退误差补偿修正方法对直接影响烟雾模拟实时性和真实性的对流项的求解步骤,从而减少计算时间.实验结果表明,采用文中方法模拟出的效果比较真实,且使基于物理方法的烟雾模拟达到了实时性的要求.