Stabilization of Rössler chaotic dynamical system using fuzzy logic control algorithm

This paper proposes a fuzzy logic control algorithm (FLCA) to stabilize the Rössler chaotic dynamical system. The fuzzy logic control system is based on a Takagi-Sugeno-Kang inference engine and the stability analysis in the sense of Lyapunov is carried out using Lyapunov’s direct method. The new FLCA is formulated to offer sufficient inequality stability conditions. The asymptotic complexity of our algorithm is analyzed and proved to be lower in comparison with that of linear matrix inequality-based FLCAs. A set of simulation results illustrates the effectiveness of the proposed FLCA.     

ASYMPTOTIC PROPERTIES OF SOME PRELIMINARY ESTIMATORS FOR AUTOREGRESSIVE MOVING AVERAGE TIME SERIES MODELS

Abstract. Some simple preliminary estimators for the coefficients of mixed autoregressive moving average time series models are considered. As the first step the estimators require the fitting of a long autoregression to the data. The first two methods of the paper are non-iterative and generally inefficient. The estimators are Yule-Walker type modifications of the least squares estimators of the coefficients in auxiliary linear regression models derived, respectively, for the coefficients of the long autoregression and for the coefficients of the corresponding long moving average approximation of the model. Both of these estimators are shown to be strongly consistent and their asymptotic distributions are derived. The asymptotic distributions are used in studying the loss in efficiency and in constructing the third estimator of the paper which is an asymptotically efficient two-step estimator. A numerical illustration of the third estimator with real data is given.     

Analysis of a large number of Markov chains competing for transitions

We consider the behaviour of a stochastic system composed of several identically distributed, but non independent, discrete-time absorbing Markov chains competing at each instant for a transition. The competition consists in determining at each instant, using a given probability distribution, the only Markov chain allowed to make a transition. We analyse the first time at which one of the Markov chains reaches its absorbing state. When the number of Markov chains goes to infinity, we analyse the asymptotic behaviour of the system for an arbitrary probability mass function governing the competition. We give conditions that ensure the existence of the asymptotic distribution and we show how these results apply to cluster-based distributed storage when the competition is handled using a geometric distribution.     

An embedding approach for the design of state‐feedback tracking controllers for references with jumps

We study the problem of designing state‐feedback controllers to track time‐varying state trajectories that may exhibit jumps. Both plants and controllers considered are modeled as hybrid dynamical systems, which are systems with both continuous and discrete dynamics, given in terms of a flow set, a flow map, a jump set, and a jump map. Using recently developed tools for the study of stability in hybrid systems, we recast the tracking problem as the task of asymptotically stabilizing a set, the tracking set, and derive conditions for the design of state‐feedback tracking controllers with the property that the jump times of the plant coincide with those of the given reference trajectories. The resulting tracking controllers guarantee that solutions of the plant starting close to the reference trajectory stay close to it and that the difference between each solution of the controlled plant and the reference trajectory converges to zero asymptotically. Constructive conditions for tracking control design in terms of LMIs are proposed for a class of hybrid systems with linear maps and input‐triggered jumps. The results are illustrated by various examples. Copyright © 2013 John Wiley & Sons, Ltd.     

一类捕食-被捕食模型解的渐近性态

对两种群的捕食-被捕食模型,利用正性定理和线性化方法,研究了一类带时滞具有阶段结构非线性反应扩散系统的牛曼初边值问题,得到了解的存在性和平衡态方程正解的局部渐近稳定的充分条件.这个结果隐含着捕食-被捕食系统的共存是持久的.     

一类有理差分方程的全局渐近稳定性

研究差分方程xn＋1=fgh＋f＋g＋h＋a/fg＋gh＋hf＋1＋a（n=0,1,…）的全局渐近稳定性,其中a∈（1,＋∞）,f=f（x-r1,…,x-rk）∈C（（0,＋∞）^k,（0,＋∞））,g=g（xn-m1,…,xn-ml）∈C（（0,＋∞）^l,（0,＋∞））,h=h（xn-s1,…,xn-sσ）∈C（（0,＋∞）^σ,（0,＋∞））,k,lσ∈{1,2,…},0≤r1〈…〈rk,0≤m1〈…〈ml,0≤s1〈…〈sσ,并且初值为正实数．给出了该方程关于唯一正平衡点=↑x=1的全局稳定的充分条件,推广了参考文献[5]-[7]中的一些结果．     

缺失数据下m相依样本的大样本性质

讨论了缺失数据在随机补充方式下均值的估计,证明了估计的相合性和渐进正态性,并给出了经验似然比统计量的渐进分布．     

一类带谱参数的奇异Sturm-Liouville算子特征的渐近分析工

研究了一类具有转换条件且在一个边界条件中带谱参数的奇异Sturm—Liouville问题．将上述问题的基本解的渐近分析,转化为考虑定义在适当的Hilbert空间H中的一个线性算子A的基本解的渐近分析,同时推导出该奇异的Sturm-Liouville算子A的基本解的渐近式．     

一类差分方程的渐近概周期序列解的存在性

利用渐近概周期函数以及序列的定义和基本性质,得出下面离散系统存在正渐近概周期序列解唯一性的充分条件.     

一类有理差分方程的全局渐近稳定性

通过研究一类有理差分方程的唯一的正平衡解的性态,进一步证明了此类差分方程的唯一正平衡解是全局渐近稳定的.