On the analysis of nonlinear nilpotent switched systems using the Hall–Sussmann system

We consider an open problem on the stability of nonlinear nilpotent switched systems posed by Daniel Liberzon. Partial solutions to this problem were obtained as corollaries of global nice reachability results for nilpotent control systems. The global structure is crucial in establishing stability. We show that a nice reachability analysis may be reduced to the reachability analysis of a specific canonical system, the nilpotent Hall–Sussmann system. Furthermore, local nice reachability properties for this specific system imply global nice reachability for general nilpotent systems. We derive several new results revealing the elegant Lie-algebraic structure of the nilpotent Hall–Sussmann system.     

Necessary conditions of optimality for a class of optimal control problems on time scales

A class of optimal control problems of a system governed by linear dynamic equations on time scales with quadratic cost functional is considered. By the Lebesgue Δ-integral theory and the Sobolev-type space H¹ on time scales the weak solution of linear dynamic equations on time scales for both initial value problem and backward problem are introduced, therefore the necessary conditions of optimality are presented. Some typical examples are given for demonstration.     

Linear Image Reconstruction by Sobolev Norms on the Bounded Domain

The reconstruction problem is usually formulated as a variational problem in which one searches for that image that minimizes a so called prior (image model) while insisting on certain image features to be preserved. When the prior can be described by a norm induced by some inner product on a Hilbert space, the exact solution to the variational problem can be found by orthogonal projection. In previous work we considered the image as compactly supported in and we used Sobolev norms on the unbounded domain including a smoothing parameter γ>0 to tune the smoothness of the reconstructed image. Due to the assumption of compact support of the original image, components of the reconstructed image near the image boundary are too much penalized. Therefore, in this work we minimize Sobolev norms only on the actual image domain, yielding much better reconstructions (especially for γ≫0). As an example we apply our method to the reconstruction of singular points that are present in the scale space representation of an image.     

一种时延受限的最优时延抖动路由算法

研究多播端到端时延受限条件下的最优时延抖动问题,提出一种有效的多播路由算法。通过修改源节点到目的节点的路径,使时延较小的目的节点获得尽可能大的时延值,时延较大的目的节点获得尽可能小的时延值。仿真结果表明,该算法能获得较小的时延抖动。     

一种复杂模式网传数据软件模拟器的设计

针对某型远程监控系统复杂、数据量大、数据结构多变等给软件设计带来的难度,设计了一个软件模拟器,构成闭环调试系统,利于检查实战软件。该模拟器以XML技术为核心,综合了数据帧编排、软件界面自动生成、用户控件定制等先进技术,有效对监视对象进行了模拟,实现了多模式下数据的自动组帧和发送功能。通过该模拟器的配合,发现实战软件设计缺欠,具有很好的推广应用价值。     

改进的验证正确性ACTL性质的限界模型检测方法

近些年来,基于SAT的限界模型检测方法作为基于BDD的限界模型检测方法的一种有效补充,已经得到了一定的发展。其中,大部分的研究成果都集中在了使用该方法来进行系统查错方面,而在正确性性质的验证上一直难有突破,原因在于正确性性质的验证依赖于一个完备上界,而这个完备上界在限界模型检测方法中很难实现。对传统限界模型检测中的编码方式进行相应改变,就能够在一定程度上解决这一问题,进行正确性性质的验证。在此基础上对该编码方法进行改进,从而提高它的求解效率,扩大其应用领域。     

Restricted compositions and permutations: From old to new Gray codes

Any Gray code for a set of combinatorial objects defines a total order relation on this set: x is less than y if and only if y occurs after x in the Gray code list. Let ? denote the order relation induced by the classical Gray code for the product set (the natural extension of the Binary Reflected Gray Code to k-ary tuples). The restriction of ? to the set of compositions and bounded compositions gives known Gray codes for those sets. Here we show that ? restricted to the set of bounded compositions of an interval yields still a Gray code. An n-composition of an interval is an n-tuple of integers whose sum lies between two integers; and the set of bounded n-compositions of an interval simultaneously generalizes product set and compositions of an integer, and so ? put under a single roof all these Gray codes.As a byproduct we obtain Gray codes for permutations with a number of inversions lying between two integers, and with even/odd number of inversions or cycles. Such particular classes of permutations are used to solve some computational difficult problems.     

限制树宽图上的有界聚类

有界聚类问题源于II3M研究院开发的一个分布式流处理系统,即S系统。问题的输入是一个点赋权和边赋权的无向图,并指定若干个称为终端的顶点。称顶点集合的一个子集为一个子类。子类中所有顶点的权和加上该子类边界上所有边的权和称为该子类的费用。有界聚类问题是要得到所有顶点的一个聚类,要求每个子类的费用不超过给定预算召,每个子类至多包含一个终端,并使得所有子类的总费用最小。对于限制树宽图上的有界聚类问题,给出了拟多项式时间精确算法。利用取整的技巧对该算法进行修正,可在多项式时间之内得到(1+ε)-近似解,其中每个子类的费用不超过(1+ε)B,:是任意小的正数。如果进一步要求每个子类恰好包含一个终端,则所给算法可在多项式时间之内得到(1+ε)-近似解,其中每个子类的费用不超过(2+ε)B。