Input‐output triggered control using ‐stability over finite horizons

This paper investigates stability of nonlinear control systems under intermittent information. Following recent results in the literature, we replace the traditional periodic paradigm, where the up‐to‐date information is transmitted and control laws are executed in a periodic fashion, with the event‐triggered paradigm. Building on the small gain theorem, we develop input–output triggered control algorithms yielding stable closed‐loop systems. In other words, based on the currently available (but outdated) measurements of the outputs and external inputs of a plant, a mechanism triggering when to obtain new measurements and update the control inputs is provided. Depending on the noise in the environment, the developed algorithm yields stable, asymptotically stable, and ‐stable (with bias) closed‐loop systems. Control loops are modeled as interconnections of hybrid systems for which novel results on ‐stability are presented. The prediction of a triggering event is achieved by employing ‐gains over a finite horizon. By resorting to convex programming, a method to compute ‐gains over a finite horizon is devised. Finally, our approach is successfully applied to a trajectory tracking problem for unicycles. Copyright © 2014 John Wiley & Sons, Ltd.     

On the Controllability of Nonlocal Second‐Order Impulsive Neutral Stochastic Integro‐Differential Equations with Infinite Delay

In this paper, we investigate the controllability for a class of nonlocal second‐order impulsive neutral stochastic integro‐differential equations with infinite delay in Hilbert spaces. More precisely, a set of sufficient conditions for the controllability results of nonlocal second‐order impulsive neutral stochastic integro‐differential equations with infinite delay are derived by means of the Banach fixed point theorem combined with theories of a strongly continuous cosine family of bounded linear operators. As an application, an example is provided to illustrate the obtained theory.     

A comment on the “Robust stability analysis of fractional order interval polynomials”, by Nusret Tan et al.

It is shown that Theorem 3 in the article mentioned in the title is not true and some modification is suggested to eliminate the mistake.     

Complete controllability for abstract measure differential systems

In this paper, we investigate the complete controllability for abstract measure differential systems. Firstly, we introduce several new concepts about complete controllability for abstract measure differential systems. Then, on the basis of the Sadovskii fixed‐point theorem, we give sufficient conditions for complete controllability for a class of abstract measure differential systems. The compactness of the semigroup generated by some operator is unnecessary in this paper, and we show that our results, dealing with complete controllability problem for an ordinary differential system in infinite‐dimensional Banach space, are also less conservative than that in the previous literature. Copyright © 2012 John Wiley & Sons, Ltd.     

On stability delay bounds of simple input-delayed linear and non-linear systems: Computational results

This paper deals with the problem of delay size stability analysis of single input-delayed linear and nonlinear systems. Conventional reduction, reduction linked by sliding mode, and linear memoryless control approaches are used for simple input-delayed systems to obtain the stability conditions. Several first order examples are investigated systematically to demonstrate the capabilities and limitations of the advanced stability analysis techniques including Lyapunov-Krasovskii functionals, Newton-Leibniz formula, and a newly addressed Lagrange mean value theorem. Numerical comparative results show the usefulness and effectiveness of the advanced delay size analysis techniques proposed in this paper.     

突变理论在堤防安全综合评价中的应用

堤防工程安全受洪水、地震、堤身土质及堤基结构等多种因素影响,且其作用机理复杂,一旦失事危害巨大.将突变理论引入堤防工程安全评价中,根据突变评价原理,建立了堤防工程安全综合评价指标体系,参照大坝安全评价标准,结合堤防工程特点,建立了堤防工程安全等级划分标准,利用突变评价的归一公式计算了北江大堤石角堤段设计洪水情况的安全评价指标值,根据等级划分标准,从计算结果分析得知该段堤防在设计洪水工况下安全性较高,为堤防工程安全管理提供科学依据.     

知识的属性扰动规律的不等式关系

知识的属性扰动引起知识规律的变化,这些变化的规律称为扰动规律.利用单向S-粗集和单向S-粗集对偶,给出属性扰动的知识规律的上规律.下规律的概念,并对知识规律与属性扰动的知识规律进行了讨论,提出了属性扰动知识规律(上规律,下规律)的不等式定理.     

S-粗集与数据挖掘单位圆特征

给出单向S-粗集(one direction singular rough sets)、单向S-粗集对偶(dual of one direction singular rough sets)的结构。单向S-粗集与单向S-粗集对偶是改进Z.Pawlak粗集得到的,单向S-粗集与单向S-粗集对偶具有动态特性。给出单向S-粗集、单向S-粗集对偶与Z.Pawlak粗集的关系。S-粗集具有三类形式:单向S-粗集、单向S-粗集对偶、双向S-粗集,利用单向S-粗集、单向S-粗集对偶,给出数据内挖掘、数据外挖掘概念,给出数据内挖掘的外同心圆定理、数据外挖掘的内同心圆定理,并给出其应用。S-粗集是粗集理论与应用研究的新分支。     

Automatic Construction and Verification of Isotopy Invariants

We extend our previous study of the automatic construction of isomorphic classification theorems for algebraic domains by considering the isotopy equivalence relation. Isotopism is an important generalisation of isomorphism, and is studied by mathematicians in domains such as loop theory. This extension was not straightforward, and we had to solve two major technical problems, namely, generating and verifying isotopy invariants. Concentrating on the domain of loop theory, we have developed three novel techniques for generating isotopic invariants, by using the notion of universal identities and by using constructions based on subblocks. In addition, given the complexity of the theorems that verify that a conjunction of the invariants form an isotopy class, we have developed ways of simplifying the problem of proving these theorems. Our techniques employ an interplay of computer algebra, model generation, theorem proving, and satisfiability-solving methods. To demonstrate the power of the approach, we generate isotopic classification theorems for loops of size 6 and 7, which extend the previously known enumeration results. This work was previously beyond the capabilities of automated reasoning techniques. The author’s work was supported by EPSRC MathFIT grant GR/S31099.     

A generalization of the Curtis–Hedlund theorem

Let A be a set and let G be a group, and equip A^G with its prodiscrete uniform structure. Let τ:A^G→A^G be a map. We prove that τ is a cellular automaton if and only if τ is uniformly continuous and G-equivariant. We also give an example showing that a continuous and G-equivariant map τ:A^G→A^G may fail to be a cellular automaton when the alphabet set A is infinite.