Bounded Consensus Algorithms for Multi‐Agent Systems in Directed Networks

In this paper, the consensus problem is investigated via bounded controls for the multi‐agent systems with or without communication. Based on the nested saturation method, the saturated control laws are designed to solve the consensus problem. Under the designed saturated control laws, the transient performance of the closed‐loop system can be improved by tuning the saturation level. First of all, asymptotical consensus algorithms with bounded control inputs are proposed for the multi‐agent systems with or without communication delays. Under these consensus algorithms, the states’ consensus can be achieved asymptotically. Then, based on a kind of novel nonlinear saturation functions, bounded finite‐time consensus algorithms are further developed. It is shown that the states’ consensus can be achieved in finite time. Finally, two examples are given to verify the efficiency of the proposed methods.     

Geometrically non-linear behavior of structural systems with random material property: An asymptotic spectral stochastic approach

An asymptotic spectral stochastic approach is presented for computing the statistics of the equilibrium path in the post-bifurcation regime for structural systems with random material properties. The approach combines numerical implementation of Koiter’s asymptotic theory with a stochastic Galerkin scheme and collocation in stochastic space to quantify uncertainties in the parametric representation of the load–displacement relationship, specifically in the form of uncertain post-buckling slope, post-buckling curvature, and a family of stochastic displacement fields. Using the proposed method, post-buckling response statistics for two plane frames are obtained and shown to be in close agreement with those obtained from Monte Carlo simulation, provided a fine enough spectral representation is used to model the variability in the random dimension.     

Further remarks for the matrix type-B codes

Different philosophies lie behind the detecting and correcting error patterns in a real communication channel. The sceptic points in choosing an efficient code, specifically the matrix type-B code, were pointed out in Refs. 1 and 2.Some more points are shown here. As a result the matrix type-B code is found to be a best choice. Some more theoretical aspects for this code are also given. These are useful for the realization and testing of an encoding-decoding algorithm with IC's used in a unique way for its implementation.     

具有阶段结构和HollingⅢ型功能反应的捕食-食饵系统持久性和全局稳定性

研究一类具有HollingⅢ型功能反应函数的捕食-食饵系统模型,通过建立适当的Lyapunov泛函,对模型进行定性分析,给出了系统的持久性、全局渐近稳定性的充分条件.     

Ergodic Hyperbolic Attractors of Endomorphisms

Let μ be an SRB-measure on an Axiom A attractor Δ of a C ²-endomorphism (M, f). As is known, μ-almost every x ϵ Δ is positively regular and the Lyapunov exponents of (f, T f) at x are constants λ⁽ⁱ⁾(f, μ), 1 ≤ i ≤ s. In this paper, we prove that Lebesgue-almost every x in a small neighborhood of Δ is positively regular and the Lyapunov exponents of (f, T f) at x are the constants λ⁽ⁱ⁾(f, μ), 1 ≤ i ≤ s. This result is then generalized to nonuniformly completely hyperbolic attractors of endomorphisms. The generic property of SRB-measures is also proved. 2000 Mathematics Subject Classification. 37D20, 37D25, 37C40. This work was supported by the 973 Funds of China for Nonlinear Science, the NSFC 10271008, and the Doctoral Program Foundation of the Ministry of Education.     

A Stability Theory in Nonlinear Programming

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Security of polarization-shift keying chaos optical communication system

To evaluate the security of a chaos optical communication system employing the polarization-shift keying (PolSK) modulation technology, its chaos characteristic needs to be verified. In this paper, an analysis was done for the signal of this system. Three methods were used to judge whether the signal was maintaining chaos characteristics or not: watching the strange attractor in three-dimensional phase space, computing the largest Lyapunov exponent by the equation which meets and Wolf's method, and evaluating the self-power spectrum density function. As a result, the strange attractor was clearly watched, the largest Lyapunov exponent was positive 0.0364 and 0.0106 respectively,and the self-power spectrum was wide and continuous with the noise background. The evaluation of chaos for the signal transmitted in the system is therefore presented. On the other hand, the minimal embodied dimension of the signal was given by the false nearest neighbors (FNN) method and it reached 6, which showed the higher dimension chaos characteristics of the system.Adding the analysis of the ability of anti-attack for the system, it is concluded that the system has higher security than the normal chaos masking schemes.     

Wigner-Ville analysis of asymptotic signals and applications

The Wigner-Ville joint representation (WVJR) appears as a quite good candidate among the various time and frequency JR. This JR performs exact demodulation of finite energy signals even in presence of linear filtering. Signal or waveform synthesis may be derived from this JR or from ambiguity function. Asymptotic signals are depicted in such a way that modulation parameters may be estimated. Dealing with vibroseismic signals the WVJR allows to identify damping parameters related to propagation effects. Propagation models may be checked by this technique. An example of such a technique is provided by processing of synthetic seismic data.     

Plane Stress Steady Crack Growth in a Power-Law Hardening Material

The paper reports the results from an asymptotic analysis for a crack growing quasistatically under Mode I, plane stress conditions for a power-law hardening material. The asymptotic stress and deformation velocity fields near the growing crack tip are determined, comparisons to related work are discussed and some numerical results for aluminum are included. This revised version was published online in August 2006 with corrections to the Cover Date.     

一类交叉耦合抛物型方程组解的渐近性态

研究了一类交叉耦合抛物型方程组解的整体存在及爆破问题.首先构造方程组的上、下解,再利用比较定理,得到由幂函数和对数函数完全耦合的退化抛物型方程组解的整体存在及解在有限时刻爆破的充分条件.