机器人动力学与控制——讲座连载之四

§4 李雅普诺夫方法 RM系统的动能为 T=1/2q~TD(q)q (4.1)记广义冲量为p p=(T/q)~T=D(q)q (4.2) 式(4.1)、(4.2)中的q为RM系统的广义坐标q=[q_1,…,q_n]~T,设系统的势能为V(q),H=T+V(q)为系统的哈密顿函数,则RM动力学方程为     

进位移位寄存器序列的密码学性质

本文以进位移位寄存器(FCSR)序列及2-adic数和分母为奇素数的有理数之间的内在联系为背景,讨论了FCSR序列的密码学性质,给出以进位移位寄存器序列为周期序列的新的充分必要条件,并对一类大周期序列的状态图进行了刻画。     

线性复杂度为2n-2m-1的2n-周期二元序列的k-错线性复杂度*

线性复杂度和k-错线性复杂度是研究流密码稳定性的两个重要概念。当改变序列某几位时不会使得序列的线性复杂度急剧减少,说明该序列的稳定性良好。运用Chan-Games给出了当k=4或5时,F2上固定线性复杂度为2n-2m-1的2n-周期二元序列的k-错线性复杂度所有可能值,LCk(s)=0或LCk(s)=2n-2m-2r+1+c,LCk(s)=2n-2r+1+c。这一结果对流密码稳定性的研究有重要的应用价值。     

二元m序列的五值互相关函数

本文证明了当n=2m（m≥3,m是奇数）、采样因子d=2^m＋3时,二元m序列与其采样序列的互相关函数Cd（t）必取集合{-1,3·2^m-1,2^m＋1-1,2^m-1,-2^m-1}中的每一个值,并给出了它们各自的分布。     

可达性等价于状态方程可满足性的petri网子类

定义了一个petri网子类:PN=(S,T;F,M0),满足条件s∈S→｜·s｜≤1。证明:当目标标识Md>0时,此petri网子类的可达性等价于状态方程Md=M0+ATX的可满足性。同时,当此petri网子类的可达性等价于状态方程可满足性时,可得出如下两点结论:(1)对于满足M0+ATX>0的每个非平凡的非负整数向量X,都■t∈Tx:M0[t>;(2)对于满足M0+ATX>0的每个非平凡的非负整数向量X,X都是PN的一个可执行向量。     

线性复杂度为2n-2m的2n-周期序列的k-错线性复杂度*

线性复杂度和k-错线性复杂度是衡量密钥序列随机性的两个重要标准,运用Chan-Games算法,得到线性复杂度为2n-2m的2n-周期二元序列的k-错线性复杂度的所有可能的值,LCk(s)=0或2n－2m－2r+1+c,2n-2r+1+c。这一结果对于进一步探讨流密码密钥序列的安全性有重要的应用价值。     

新的二元互素序列的迹表示和线性复杂度

利用周期分别为奇素数p 和q的Legendre序列构造大量新的周期为 的二元序列,根据这些序列与Legendre序列在结构上的联系,给出它们的迹表示,依据E.L. Key方法得到其线性复杂度。结果表明该类序列具有良好的符号平衡性和线性复杂度性质,作为密钥流序列可抵抗Berlekamp-Massey算法的攻击。     

TT3.0技巧两则

TT3.0中自定义搜索引擎腾讯公司的T T浏览器在国内也有很多用户,最新版是3.0。不过安装后,默认只有QQ搜索引擎,事实上,我们完全可以将自己的搜索引擎,如Google和百度等添加上去:打开C:\P r o g r a m F i l e s\T e n c e n t\T T\CustomSearch\搜索引擎导入示例.txt,然后在下方添加如下语句:"用Google搜索","http://www.google.com/search?hl=zh-CN&q=[%]&lr="用百度搜歌词","http://www.baidu.com/m?tn=baidump3lyric&ct=150994944&rn=10&word=[%]"用搜刮网搜歌曲","http://search.sogua.com/search/search.asp?key=[%]&fexe=1&…     

关于QL-、D-蕴涵的分配性方程的解

研究了[r→（t∧s）]≡[（r→t）∧（r→s）],[r→（t∨s）]≡[（r→t）∨（r→s）],[（p∧q）→r]≡[（p→r）∨（q→r）],[（p∨q）→r]≡[（p→r）∧（q→r）]4个分配性方程,它们在模糊集理论中的形式分别是I（r,T₁（t,s））=T₂（I（r,t）,I（r,s））,I（r,S₁（t,s））=S₂（I（r,t）,I（r,s））,I（T₁（p,q）,r）=S₁（I（p,r）,I（q,r））,I（S₁（p,q）,r）=T₁（I（p,r）,I（q,r））,其中p,q,r,s,t∈[0,1],T₁、T₂为任意三角模,S₁、S₂为任意三角余模,给出了I为QL-、D-蕴涵时满足分配性方程的充要条件。     

修正de Bruijn序列的线性复杂度研究

n级de Bruijn-0/1序列,就是从de Bruijn序列2ⁿ个状态中去除一个全0状态（记为de Bruijn-0）或全1状态（记为de Bruijn-1）而得到的周期为2ⁿ-1的序列。研究了de Bruijn-0和de Bruijn-1（记为de Bruijn-0/1）序列的线性复杂度特性,提出了相关的定理并给出了证明,同时给出了4~6级de Bruijn-0/1序列线性复杂度的统计数据。     

Trivium-like算法中可滑动Cube的研究

对于Trivium-like算法,cube攻击是最有效的攻击手段之一.在传统cube攻击中,攻击者主要利用线性检测等方法来寻找具有低次超多项式的cube.实验结果表明存在IV变元子集I1=(vi1,vi2,…,vid)和I2=(vi1-1,vi2-1,…,vid-1)满足pI2(k0,k1,…,kn-2)=σ(pI1(k1,k2,…,kn-1)),其中ki表示密钥变元,pI1是Cube CI1对于t时刻输出比特zt的超多项式,pI2是Cube CI2对于t+1时刻的输出比特zt+1的超多项式,并且变换\sigma将ki映射到ki-1.在本文中,称这种性质为cube的可滑动性.我们研究了Trivium-like算法的攻击中cube的可滑动性.特别地,我们给出了cube具有可滑动性的一个充分条件.此外,我们将充分条件的判断,转化到求解混合整数线性规划(MILP)模型,在实际中能够快速判断出具有滑动性的cube.最后,我们将充分条件应用到实验cube攻击、基于分离性质的cube攻击和相关cube攻击的已有结果,验证了方法的正确性并在实验cube攻击中得到了一个803-轮Trivium的新结果.     

Rank condition for the controllability of a linear time-varying system

In this paper we study the controllability of the following linear time-varying control system x' = A(t)x + Bu(t), where A(t) = a(t)A and a(.) is a scalar function which is in general not continuous and satisfies the only condition: 0T a(s), ds 0, T>0. A and B are constant matrices of dimension n X n and n X m respectively. Under this condition, we prove that this system is controllable on [0,T] iff the usual Rank condition holds: Rank [B:AB:…:An-1B = n.     

Stability control and recurrent switching rules

Recently, it has been enlightened the interest of a class of switching rules with good properties, which are called eventually periodic: more precisely, it has been proven that a finite family of linear vector fields of can be stabilized by means of eventually periodic switching rules provided that it is asymptotically controllable and satisfies an additional finite time controllability condition. Unfortunately, simple examples point out that in general, eventually periodic switching rules are not robust with respect to state measurement errors. In this paper, we introduce a new type of switching rules with improved robustness properties, which are called recurrent switching rules. They are subject to the construction of a finite sequence of complete cones Γ₁, … ,Γ_H of . We shown that, if a stabilizing eventually periodic switching rule for is known, then Γ₁, … ,Γ_H can be constructed in such a way that is stabilized by any recurrent switching rule subject to Γ₁, … ,Γ_H. Copyright © 2012 John Wiley & Sons, Ltd.     

Time-series decomposition and forecasting

Any stationary time-series can be decomposed by means of an optimization operator, called the ζ-optimator, into several components (the time-series){Y _t ⁱ}, i =1,2,…, p, such that the first component {V _t ⁱ} t = 1,2,…,v is a smooth process having a larger autocorrelation in comparison with the original process {Y _t}, i.e. ρ_vi > ρ_y. Usually only a few such components are sufficient for approximating the time-series with good accuracy. The ζ-optimator involves a shape parameter a, so the decomposition is unique provided that a. is fixed. Since the component {V _t ¹} involves much of the useful information it can be used for computing predictors for control purposes. Thus, given the observations Y_v, Y_v-1, Y_v-2,…, a predictor of Y_v+1 is ρ_vi V _v ¹ (q) where, V_v ¹(q) = qY^v + q(1-q)² Y_v-2, …, the weights q(1-q)^r, r=0,1,2,…, decreasing rapidly as q = q(α) ε (0,1) Further, one may choose q rather than choosing α, since q(α) is a one-one mapping. Once q is fixed, the predictor ρ_v1 V _v ¹(q) is obtained in a straightforward way by using the formula above. It is shown that ρ_v1 V _v ¹(q) converges to the best predictor as α → 0. Some examples are worked out, illustrating both the decomposition and the forecasting procedures.     

Modelling Asynchrony with a Synchronous Model

The I/O automaton paradigm of Lynch and Tuttle models asynchrony through an interleaving parallel composition. The recognition that such interleaving models in fact can be viewed as special cases of synchronous parallel composition has been very limited. Let be any set of finite-state I/O automata drawing actions from a fixed finite set containing a subset . In this article we establish a translation T : to a class of -automata closed under a synchronous parallel composition, for which T is monotonic with respect to implementation relative to , and linear with respect to composition. Thus, for A¹, ..., A, B¹, ..., B and A = A¹ ... A, B = B¹ ... B, if is the set of actions common to both A and B, then A implements B (in the sense of I/O automata) if and only if the -automaton language containment (T(A¹) ... T(A)) (T(B¹) ... T(B)) obtains, where denotes the interleaving parallel composition on and denotes the synchronous parallel composition on . For the class , we use the L-process model of -automata. This result enables one to verify systems specified by I/O automata through model-checkers such as COSPAN or SMV, that operate on models with synchronous parallel composition. The translation technique generalizes to other interleaving models, although in each case, the translation map must match the specific model.     

Unextendible Product Bases and Locally Unconvertible Bound Entangled States

Mutual convertibility of bound entangled states under local quantum operations and classical communication (LOCC) is studied. We focus on states associated with unextendible product bases (UPB) in a system of three qubits. A complete classification of such UPBs is suggested. We prove that for any pair of UPBs S and T the associated bound entangled states _S and _T cannot be converted to each other by LOCC, unless S and T coincide up to local unitaries. More specifically, there exists a finite precision (S,T) > 0 such that for any LOCC protocol mapping _S into a probabilistic ensemble (p, ), the fidelity between _T and any possible final state satisfies F(_T, ) = 1 - (S,T).PACS: 03.65.Bz; 03.67.-a; 89.70+c.     

Sulla ricerca dei digrafi fortemente connessi aventi uno stesso grafo di supporto e di lunghezza generalizzata minima o massima

Sunto Assegnato un grafo finitoG ₀, notiamo con la famiglia dei digrafiG aventiG ₀ come grafo di supporto. E' noto che alla famiglia appartengono digrafi fortemente conuessi (f. c.) se e solo seG ₀ è connesso e ogni sno spigolo appartiene a qualche ciclo. Nel presente lavoro iudaghiamo sulla struttura dei digrafi fortemente connessi di una assegnata famiglia e dimostriamo come tali digrafi si possono costruire tutti a partire da uno di essi (costruito a sua volta utilizzando un algoritmo di B. Roy) mediante l'applicazione di un numero finito di trasformazioni elementari opportunamente introdotte. Se immaginiamo il grafoG ₀ come rappresentazione di una certa rete stradale, dobbiamo interpretare ogni digrafo di come un possibile orientamento a sensi unici di tutte le strade della rete. A ciascuno dei due possibili orientamenti degli spigoli della reteG ₀ è possibile associare un numero reale esprimente il costo oppure l'utilità di quell'orientamento: in tal modo ad ogni orientamento a sensi unici delle strade della rete risulta associato un costo complessivo oppure un utile complessivo. Il problema di orientare in modo ottimo gli spigoli delle reteG ₀, compatibilmente con i vincoli di percorribilità dell'intera rete, si traduce nella ricerca dei digrafi f. c. di a cui è associata una lunghezza generalizzata minima oppure massima. Noi affrontiamo tale problema e presentiamo una condizione necessaria e sufficiente di ottimo che permette di costruire mediante un opportuno algoritmo i digrafi fortemente connessi di di lunghezza generalizzata minima oppure massima.

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Given a finite graphG ₀, let be the family of digraphs that haveG ₀ as a supporting graph. It is a well established fact that contains strongly connected (s. c.) digraphs if and only ifG ₀ is connected, and if every edge ofG ₀ belongs to one or more cycles. In the present work the structure of s. c. digraphs of a given family is investigated. It is also proved that all such digraphs can be constructed from one of them (that itself is constructed by an algorithm of B. Roy), with a finite number of appropriate elementary transformations. If a graphG ₀ represents a given road network, every digraph in can be interpreted as a possible one-way orientation of all the roads in the network. One can associate with each of the orientations of the edges ofG ₀ a real number representing the cost or the gain of such an orientation: thus, with every one-way system in the network is associated a cumulative cost or a cumulative gain. The problem of the optimal orientation of the edges ofG ₀, while respecting the constraints on the viability of the entire network, becomes the search of s. c. digraphs in associated with optimal generalized lengtht. A necessary and sufficient condition for optimality is presented, that leads to the construction, by means of an appropriate algorithm, of s. c. diagraphs in with optimal generalized lenght.

     

Stability analysis of a model reference adaptive control system with sinusoidal inputs†

In this paper a rigorous method is presented for analysing an M.I.T. type model reference adaptive control system with sinusoidal inputs. The linearized equations for the adapting system, formed by using small perturbation analysis, are written in the matrix form [xdot] = A(t)x, where A(t) is periodic. This matrix equation is then integrated over one period using a Runge–Kutta technique. The transition matrix relating the value of x at the end of a period to its value at the beginning of the period is examined to see whether all its eigenvalues are within the unit circle, thus establishing stability.