一类全系数模糊线性规划的求解方法

利用结构元方法定义一种模糊数排序准则,提出将目标函数和约束条件中都含有三角模糊数的全系数模糊线性规划等价转化为经典线性规划的方法,并证明其合理性.与其它方法相比较,该方法证明了得到的解优于已有其它方法的解,并且约束条件少,运算方法简便.将本文的方法运用到数值算例中,进一步表明了提出方法的有效性和广泛性.     

On Taylor-like integral representations of analytic functions

Let f be an analytic function in a complex domain D and (without loss of generality) assume 0∈D. Then the paper’s aim is to derive a Taylor-like integral expression for f, i.e. an integral representation analogous to the corresponding power series, say, ∑ _k=0^∞ a _k t ^k /k!. We start from the simplest case f(t)=e ^t , which leads to the identity

On convergent numerical algorithms for unsymmetric collocation

In this paper, we are interested in some convergent formulations for the unsymmetric collocation method or the so-called Kansa’s method. We review some newly developed theories on solvability and convergence. The rates of convergence of these variations of Kansa’s method are examined and verified in arbitrary–precision computations. Numerical examples confirm with the theories that the modified Kansa’s method converges faster than the interpolant to the solution; that is, exponential convergence for the multiquadric and Gaussian radial basis functions (RBFs). Some numerical algorithms are proposed for efficiency and accuracy in practical applications of Kansa’s method. In double–precision, even for very large RBF shape parameters, we show that the modified Kansa’s method, through a subspace selection using a greedy algorithm, can produce acceptable approximate solutions. A benchmark algorithm is used to verify the optimality of the selection process.     

Conditioning of Random Conic Systems Under a General Family of Input Distributions

We consider the conic feasibility problem associated with the linear homogeneous system Ax≤0, x≠0. The complexity of iterative algorithms for solving this problem depends on a condition number C(A). When studying the typical behavior of algorithms under stochastic input, one is therefore naturally led to investigate the fatness of the tails of the distribution of C(A). Introducing the very general class of uniformly absolutely continuous probability models for the random matrix A, we show that the distribution tails of C(A) decrease at algebraic rates, both for the Goffin–Cheung–Cucker number C _G and the Renegar number C _R . The exponent that drives the decay arises naturally in the theory of uniform absolute continuity, which we also develop in this paper. In the case of C _G , we also discuss lower bounds on the tail probabilities and show that there exist absolutely continuous input models for which the tail decay is subalgebraic. R. Hauser was supported by a grant of the Nuffield Foundation under the “Newly Appointed Lecturers” grant scheme (project number NAL/00720/G) and through grant GR/S34472 from the Engineering and Physical Sciences Research Council of the UK. The research in this paper was conducted while T. Müller was a research student at the University of Oxford. He was partially supported by EPSRC, the Oxford University Department of Statistics, Bekker-la-Bastide fonds, Dr. Hendrik Muller’s Vaderlandsch fonds, and Prins Bernhard Cultuurfonds.     

Constrained regulation of continuous Petri nets

This paper deals with constrained regulation of continuous Petri nets under the so-called infinite servers semantics. Our aim is to design feedback gains that permit us to reach both desired stationary marking vector and desired asymptotic firing rate vector. The proposed approach takes into account constraints on the control, the marking of the Petri net, and the stability of the closed-loop system. The existence of a solution is first expressed geometrically, in terms of the inclusion of two polyhedral sets. They are reformulated algebraically as linear matrix inequalities, which provides an effective way to calculate feedback gains answering the problem. Finally, an application to an assembly production system is given.     

Fuzzy guaranteed cost controller for trajectory tracking in nonlinear systems

In this paper, we propose a fuzzy logic based guaranteed cost controller for trajectory tracking in nonlinear systems. Takagi–Sugeno (T–S) fuzzy model is used to represent the dynamics of a nonlinear system and the controller design is carried out using this fuzzy model. State feedback law is used for building the fuzzy controller whose performance is evaluated using a quadratic cost function. For designing the fuzzy logic based controller which satisfies guaranteed performance, linear matrix inequality (LMI) approach is used. Sufficient conditions are derived in terms of matrix inequalities for minimizing the performance function of the controller. The performance function minimization problem with polynomial matrix inequalities is then transformed into a problem of minimizing a convex performance function involving standard LMIs. This minimization problem can be solved easily and efficiently using the LMI optimization techniques. Our controller design method also ensures that the closed-loop system is asymptotically stable. Simulation study is carried out on a two-link robotic manipulator tracking a reference trajectory. From the results of the simulation study, it is observed that our proposed controller tracks the reference trajectory closely while maintaining a guaranteed minimum cost.     

A problem in enumerating extreme points, and an efficient algorithm for one class of polytopes

We consider the problem of developing an efficient algorithm for enumerating the extreme points of a convex polytope specified by linear constraints. Murty and Chung (Math Program 70:27–45, 1995) introduced the concept of a segment of a polytope, and used it to develop some steps for carrying out the enumeration efficiently until the convex hull of the set of known extreme points becomes a segment. That effort stops with a segment, other steps outlined in Murty and Chung (Math Program 70:27–45, 1995) for carrying out the enumeration after reaching a segment, or for checking whether the segment is equal to the original polytope, do not constitute an efficient algorithm. Here we describe the central problem in carrying out the enumeration efficiently after reaching a segment. We then discuss two procedures for enumerating extreme points, the mukkadvayam checking procedure, and the nearest point procedure. We divide polytopes into two classes: Class 1 polytopes have at least one extreme point satisfying the property that there is a hyperplane H through that extreme point such that every facet of the polytope incident at that extreme point has relative interior point intersections with both sides of H; Class 2 polytopes have the property that every hyperplane through any extreme point has at least one facet incident at that extreme point completely contained on one of its sides. We then prove that the procedures developed solve the problem efficiently when the polytope belongs to Class 2.     

A thin-film model for corotational Jeffreys fluids under strong slip

We derive a thin-film model for viscoelastic liquids under strong slip which obey the stress tensor dynamics of corotational Jeffreys fluids.     

基于线性方程组数学分离模型建立光纤传感过程检测复方缬沙坦氢氯噻嗪片溶出度

基于线性方程组数学分离模型建立在线过程检测复方缬沙坦氢氯噻嗪片溶出度方法。分别扫描缬沙坦和氢氯噻嗪的紫外吸收光谱,两组分在最大吸收波长处完全重叠。根据朗伯比尔定律吸光度加和性原理,分别测定两组分在最大吸收波长处的吸光系数,建立线性方程组数学分离模型,采用光纤传感过程分析技术(FODT)检测缬沙坦氢氯噻嗪片的溶出度,并与HPLC法相比较。在规定的溶出介质中,两种成分同时实时测定,并且FODT累积溶出度与HPLC法相比较结果无显著性差异(p>0.05)。不同批次药物的溶出行为一致,说明制剂工艺稳定,均匀度好。溶出曲线显示缬沙坦溶出快于并高于氢氯噻嗪,且30 min时两组分的溶出度均大于80%符合美国药典规定。结果表明,应用线性方程组数学分离模型结合FODT法可实现复方缬沙坦氢氯噻嗪片中双组分溶出度的同时检测,并可提供双组分的溶出过程曲线和全部溶出数据,直观反映各组分在各溶出时段的快慢,为此药建立标准提供依据。与HPLC法单点数据相比优势明显,更有利于药品评价和抽验质量分析。