Invariance of the aperiodic property for polynomials with perturbedcoefficients

A procedure for obtaining the maximal intervals of the coefficients for a perturbed polynomial to be still strictly aperiodic is presented. Lemmas, theorems, and proofs are given. An illustrative example is presented     

Strict Hurwitz property of polynomials under coefficientperturbation

A simple procedure for computing the allowable interval coefficient perturbations of a strictly stable polynomial is presented. The amount of computations involved is very little, while the procedure is able to handle the case where the relative uncertainty of the polynomial coefficients are not known. It can also handle the case of linearly dependent parameter uncertainties. The procedure can also be modified to treat the case of simple nonlinear dependent parameter uncertainties. The details of the modified procedure will depend on the nature of the nonlinearity     

Aperiodic property of interval polynomials

An examination is made of the aperiodic property of interval polynomials. The authors also characterize the zero locations of aperiodic interval polynomials. Examples are given that clarify the points made     

Invariance of the strict Hurwitz property for polynomials with perturbed coefficients

Given a strictly Hurwitz polynomialf(lambda) = lambda^{n} + a_{n-1} lambda^{n-1} + a_{n-2}lambda^{n-2}+...+ a_{1}lambda + a_{0}, it is of interest to know how much the coefficients aican be perturbed while simultaneously preserving the strict Hurwitz property. For systems withn leq 4, maximal intervals of the aiare given in a recent paper by Guiver and Bose [1]. In this note, a theorem of Kharitonov is exploited to obtain a general result for polynomials of any degree.     

Convergence property of interval matrices and interval polynomials

In association with robust control-system design and analysis, the Hurwitz property of interval matrices and interval polynomials has recently been actively investigated. However, its discrete counterpart, the convergence property, has seemingly not been much discussed. In this paper, this property is studied in comparison with the Hurwitz counterpart. Some conditions under which interval matrices or interval polynomials are convergent are derived.     

Invariance of a strict Hurwitz property for uncertain polynomials with dependent coefficients

This note is concerned with the invariance of strict Hurwitz property for uncertain polynomials having dependent coefficients. A feasible test criterion is provided which reduces the conservatism of the Kharitonov theorem.     

Comments on ‘Convergence property of interval matrices and interval polynomials’

This note shows that the discrete linear interval system result of Mori and Kokame (1987) is also applicable to linear discrete time systems with linearly dependent perturbations.     

Stability analysis of systems with aperiodic sample-and-hold devices

Motivated by the widespread use of networked and embedded control systems, improved stability conditions are derived for sampled-data feedback control systems with uncertainly time-varying sampling intervals. The results are derived by exploiting the passivity-type property of the operator arising in the input-delay approach to the system in addition to the gain of the operator, and are hence less conservative than existing ones.     

Schedulability analysis of periodic and aperiodic tasks with resource constraints

In this paper, we address the problem of scheduling hybrid task sets consisting of hard periodic and soft aperiodic tasks that may share resources in exclusive mode in a dynamic environment, where tasks are scheduled based on their deadlines. Bounded blocking on exclusive resources is achieved by means of a dynamic resource access protocol which also prevents deadlocks and chained blocking. Aperiodic responsiveness is enhanced by an efficient servicing technique which assigns each aperiodic request a suitable deadline. Feasibility conditions are extended to handle tasks with deadlines different from periods and a reclaiming technique is presented to deal with early completions.     

Passivity-based non-fragile control for Markovian jump systems with aperiodic sampling

In this paper, the problem of non-fragile passive control for Markovian jump systems with aperiodic sampling is investigated. The considered controller is assumed to have either additive or multiplicative norm-bounded uncertainties. A time-dependent Lyapunov functional capturing the available information of the sampling pattern is constructed to derive a sufficient condition for non-fragile stochastic passivity of the resultant closed-loop system. Based on the condition, a mode-independent state feedback sampled-data controller is designed such that for all admissible uncertainties the closed-loop system is robustly stochastically passive. Two illustrative examples are included to demonstrate the effectiveness and merits of the proposed techniques.     

Sparse hierarchical regression with polynomials

Machine Learning - We present a novel method for sparse polynomial regression. We are interested in that degree r polynomial which depends on at most k inputs, counting at most $$\ell$$ monomial...     

严肃遇到傻瓜

导语 “我是一个艺术家，既绘画，也玩黏土、玩偶、雕塑，甚至包装设计也做。虽分属不同领域，但它们都有一个关键点——包装。相信我，包装在当代的重要性已不亚于产品本身，甚至凌驾于它之上。香水就是个好例子，它只是有味道的液态水罢了，现代人之所以买它，很重要的一个原因是为其精美的包装或附送的礼品所诱惑。如今，甚至更有用黄金王冠作包装的香水……而我的工作，就是不用黄金，也能吸引你去购买。”     

Stability of polynomials with conic uncertainty

In this paper we describe a conic approach to the stability theory of uncertain polynomials. We present necessary and sufficient conditions for a conic setp ₀+K of polynomials to be Hurwitz stable (K is a convex cone of polynomials of degree n and degp ₀=n). As analytical tools we derive an edge theorem and Rantzer-type conditions for marginal stability (semistability). The results are applied to prove an extremal-ray result for conic sets whose cone of directions is given by an interval polynomial.The second author would like to thank the Deutsche Forschungsgemeinschaft (DFG) for its support during the writing of this paper.     

B样条曲面在严格约束状态下的光顺拟合

提出一种新的B样条曲面造型方法:光顺地拟合空间型值点且同时严格地通过其中部分点.运用Lagrange乘子的条件极值法并引入光顺加权项，求出位置偏离和形状弯曲的最小二乘解，可以得到被称为B样条光顺准拟合的良好造型曲面.这一方法在包含门窗的交通工具外壳曲面设计、机械产品装配联接件制造中具有明显的实用价值.     

严格服务等级约定的区分Web服务技术研究

随着Internet的普及和Web应用的发展，满足客户不同业务需求成为人们关注的问题．该文基于业务类的访问资源需求和服务等级给出了一种资源划分策略，用来确定业务类在访问率波动较小条件下达到服务级别所需的资源；提出一种资源效用控制机制，用来适应访问的突发性和保证业务类服务等级要求．通过按周期进行资源划分，同时利用资源控制机制来适应周期内的访问突发，得到了严格服务等级约定的区分Web服务(简称SLADS)．文章通过建立原型与其它方法进行了实验比较，结果表明SLADS方法能够有效支持业务类的严格服务等级和提高资源利用率．     

Slack-based multiprocessor scheduling of aperiodic real-time tasks

We provide a constant time schedulability test and priority assignment algorithm for an on-line multiprocessor server handling aperiodic tasks. The so called Dhall’s effect is avoided by dividing tasks in two priority classes based on their utilization: heavy and light. The improvement in this paper is due to assigning priority of light tasks based on slack—not on deadlines. We prove that if the load on the multiprocessor stays below \((3 - \sqrt{5} )/2 \approx 38.197\%\), the server can accept an incoming aperiodic task and guarantee that the deadlines of all accepted tasks will be met. This is better than the current state-of-the-art algorithm where the priorities of light tasks are based on deadlines (the corresponding bound is in that case 35.425%).The bound \((3 - \sqrt{5} )/2\) can be improved if the number of processors m is known. There is a formula for the sharp bound \(U_{\mathit{threshold}}(m) = \frac{3m - 2 - \sqrt{5m^{2} - 8m + 4}}{2(m - 1)}\), which converges to \((3 - \sqrt{5} )/2\) from above as m→∞. For m≥3, the bound is higher (i.e., better) than the corresponding sharp bound for the state-of-the-art algorithm where the priorities of light tasks are based on deadlines.A simulation study also indicates that when m>3 the best effort behavior of the priority assignment scheme suggested here is better than that of the traditional scheme where priorities are based on deadlines.     

Supervisory control for fault-tolerant scheduling of real-time multiprocessor systems with aperiodic tasks

Supervisory control theory is a well-established theoretical framework for feedback control of discrete event systems whose behaviours are described by automata and formal languages. In this article, we propose a formal constructive method for optimal fault-tolerant scheduling of real-time multiprocessor systems based on supervisory control theory. In particular, we consider a fault-tolerant and schedulable language which is an achievable set of event sequences meeting given deadlines of accepted aperiodic tasks in the presence of processor faults. Such a language eventually provides information on whether a scheduler (i.e., supervisor) should accept or reject a newly arrived aperiodic task. Moreover, we present a systematic way of computing a largest fault-tolerant and schedulable language which is optimal in that it contains all achievable deadline-meeting sequences.     

Scheduling aperiodic tasks in dynamic priority systems

In this paper we present five new on-line algorithms for servicing soft aperiodic requests in realtime systems, where a set of hard periodic tasks is scheduled using the Earliest Deadline First (EDF) algorithm. All the proposed solutions can achieve full processor utilization and enhance aperiodic responsiveness, still guaranteeing the execution of the periodic tasks. Operation of the algorithms, performance, schedulability analysis, and implementation complexity are discussed and compared with classical alternative solutions, such as background and polling service. Extensive simulations show that algorithms with contained run-time overhead present nearly optimal responsiveness.A valuable contribution of this work is to provide the real-time system designer with a wide range of practical solutions which allow to balance efficiency against implementation complexity.     

Damping margins of polynomials with perturbed coefficients

Considers the polynomial P(s)=t₀ Sⁿ+t₁ S^n-1 +···+t_n where 0<a _j⩽t_j⩽b_j. Recently, V.L. Kharitonov (1978) derived a necessary and sufficient condition for this polynomial to have only zeros in the open left-half plane. Two lemmas are derived to investigate the existence of theorems similar to the theorem of Kharitonov. Using these lemmas, the theorem of Kharitonov is generalized for P(s) to have only zeros within a sector in the complex plane. The aperiodic case is also considered