基于代数正规型构造的代数免疫最优布尔函数

现有代数免疫最优布尔函数的构造方法大多基于支撑集,通过代数正规型直接构造的方法研究较少.为此,利用代数正规型的多项式表示构造一类代数免疫性质优的布尔函数,研究其代数次数、代数免疫阶、函数重量、非线性度等性质,分析采用这种方法构造的代数免疫最优布尔函数的性质及计数等结果.由构造方法可以得到代数免疫最优的布尔函数,其中包含一些已有的特殊构造结果,表明该方法更具有一般性,包含更多具有最优代数免疫阶的函数.     

An Algebraic QoS-Based Resource Allocation Model for Competitive Multimedia Applications

A new class of multimedia applications require new mechanisms to consider various Quality of Services with respect to resource constraints so that they could support reliable services and utilize available resources optimally. In this paper we present a new analytical and generic resource management model that is QoS-based. The approach for resource allocation and relevant algorithms is based on a mathematically proved model that manages resource and QoS allocation intelligently so that the total system utility of is maximized. We use the constructs of application benefit functions and resource demand functions to represent the system configuration and to solve the resource allocation problems. Extensive surveys on the related work including systematic and analytical approaches are also presented.     

Linear quadratic Nash game-based tracker for multiparameter singularly perturbed sampled-data systems: digital redesign approach

In this paper, a linear quadratic Nash game-based tracker for multiparameter singularly perturbed sample-data systems is developed. A generalized cross-coupled multiparameter algebraic Riccati equation (GCMARE) with two quadratic cost functions is solved by applying the LQR design methodology for the optimal tracker design. Firstly, the asymptotic expansions of the GCMARE are newly established, and the proposed algorithm is able to effectively solve the GCMARE with the quadratic convergence rate. Then, the low-gain digital controller with a high design performance is realized through the prediction-based digital redesign method. Finally, for further improving the tracking performance, the chaos-evolutionary-programming algorithm (CEPA) is utilized to optimally tune the parameters of the tracker. An example is presented to demonstrate the effectiveness of the proposed methodology.     

Algebraic criteria for consensus problems of continuous-time networked systems

This article addresses algebraic criteria for consensus problems of continuous-time networked systems with fixed and switching topology. A special eigenvector ω of the Laplacian matrix is first constructed and correlated with the connectivity of digraph. And then, some necessary and/or sufficient algebraic conditions are presented by employing the vector ω, which can directly determine whether the consensus problem can be solved. More importantly, for the switching topology case, the obtained algebraic conditions for the average consensus problem are necessary and sufficient. Furthermore, the presented results clearly show that only the agents corresponding to the positive elements of ω contribute to the group decision value and decide the collective behaviour of the system. Particularly for the fixed topology case, the role of each agent is exactly measured by the value of the corresponding element of ω. Based on these results, some extended protocols are further proposed to solve the average consensus problem, in which the interaction digraphs are not needed to be balanced. Numerical examples are included to illustrate the obtained results.     

Leader-following consensus of high-order multi-agent linear systems with bounded transmission channels

The leader-following consensus of high-order multi-agent linear systems with bounded transmission channels is considered. Agents modelled as LTI dynamics exchange information according to a network which can be described as a graph with agents as its vertices and information transmission channels as its edges. The transmission channels are bounded. The objective is leader-following in the sense that the state of all agents should converge to that of the leader vehicle. Detailed analysis of the leader-following consensus under bounded transmission channels is investigated for both fixed and switching network topologies.     

Adaptive linear finite-element method for modelling nonlinear dynamic systems

This paper proposes a method of identifying nonlinear dynamic models with observation data (or a training data set) which exhibits a simple structure, adaptive input-space partition and fast convergence. The method employs the multiscale approximation concepts which have been introduced in numerical analysis motivated by wavelet analysis concepts. The partition or equivalently scaled basis functions are determined and selected adaptively in a sequenced and ordered manner. This method may be also considered as a single-layer neural network but with adaptive neural neurons. The number of multiscale basis functions required depends on the degree of nonlinearity of the system being modelled. The method is compared with the cerebellar model with interpolation (CEINT) and the cerebellar model articulation control (CMAC) methods and has been shown to achieve comparative modelling accuracies but with a reduced memory space and a concomitantly reduced training set.     

Algebraic criteria for structure identification and behaviour analysis of signed networks

This paper deals with the problem on how to algebraically identify structure properties and characterise dynamic behaviours of signed networks with cooperative and antagonistic interactions. A signed digraph is employed to represent the two competitive classes of interactions, and an algebraic criterion based on the determinant of its Laplacian matrix is exploited to examine whether it is r-structurally balanced or unbalanced. Given the r-structural balance condition, an indicator vector is constructed to calculate the steady states of signed networks. This vector particularly helps to distinguish rooted nodes and non-rooted nodes from all nodes of signed digraphs, determine the connectivity of signed digraphs and develop algebraic criteria for weight balance and sign-average consensus of signed networks. Further, an algorithm via algebraic manipulations is proposed to identify the structural balance and unbalance of signed digraphs, which contributes to achieving behaviour analysis of signed networks. Simulations are included to illustrate validity of the proposed algebraic criteria.     

5轮Salsa20的代数-截断差分攻击

Salsa20 流密码算法是Estream 最终胜出的7 个算法之一.结合非线性方程的求解及Salsa20 的两个3 轮高概率差分传递链,对5 轮Salsa20 算法进行了代数-截断差分攻击.计算复杂度不大于O(2¹⁰⁵),数据复杂度为O(2¹¹),存储复杂度为O(2¹¹),成功率为97.72%.到目前为止,该攻击结果是对5 轮Salsa20 算法攻击最好的结果.     

Explicit Solution for a Class of Discrete‐Time Algebraic Riccati Equations

In the present paper we obtain an explicit closed‐form solution for the discrete‐time algebraic Riccati equation (DTARE) with vanishing state weight, whenever the unstable eigenvalues are distinct. We discuss links to current algorithmic solutions and observe that the AREs in such a class solve on one hand the infimal signal‐to‐noise ratio (SNR) problem, whilst on the other hand, in their dual form they solve a Kalman filter problem. We then extend the main result to an example case of the optimal linear quadratic regulator gain. We relax some of the assumptions behind the main result and conclude with possible future directions for the present work.     

L-fuzzy闭包算子及其等价刻画

借助L-fuzzy映射和L-fuzzy集的像,给出了由L-fuzzy映射诱导的L-fuzzy闭包算子及其等价刻画.当L为有限分配格时,讨论了代数的L-fuzzy闭包算子及其所诱导的闭包系统的等价刻画.