p-moment stability of stochastic impulsive differential equations and its application in impulsive control

The exponential p-moment stability of stochastic impulsive differential equations is addressed. A new theorem to ensure the p-moment stability is established for the trivial solution of the stochastic impulsive differential system. As an application of the theorem proposed, the problem of controlling chaos of Lorenz system which is excited by parameter white-noise excitation is considered using impulsive control method. Finally, numerical simulation results are given to verify the feasibility of our approach. Supported by the National Natural Science Foundation of China (Grant No. 10772046)     

Two-stage stochastic minimum cost consensus models with asymmetric adjustment costs

When dealing with consensus cost problems with asymmetric adjustment costs, the uncertain scenarios with certain probabilities which are becoming a serious problem decision-makers have to face. However, existing optimization-based consensus models have failed to consider uncertain factors that could influence the final consensus and total consensus cost. In order to better deal with these issues, it is necessary to develop practical consensus optimal models. Thus, we establish three two-stage stochastic minimum cost consensus models with asymmetric adjustment costs that may eventually lead the way to better consensus outcomes. The impact of uncertain parameters (such as individual opinions, unit asymmetric adjustment costs, compromise limits, cost-free thresholds) are investigated by modeling three kinds of uncertain consensus models. We solve the proposed two-stage stochastic consensus problem iteratively using the L-shaped algorithm and show the convergence of the algorithm. Furthermore, a case of pollution control negotiations verifies the practicability of the proposed models. Moreover, the comparison of results with the L-shaped algorithm and CPLEX shows that the L-shaped algorithm is more effective in solving time. Some discussions and comparisons on local and global sensitivity analysis of the uncertain parameters are presented to reveal the features of the proposed models. Finally, the relationships between the minimum cost consensus model and minimum cost consensus models with asymmetric adjustment costs and the proposed models are also provided.     

Estimation of access failure probability in D2D underlaid cellular networks

Device-to-Device (D2D) communication can reduce the mobile devices' energy consumption and increase the spectral efficiency in D2D underlaid cellular networks. However, D2D users will interfere with co-channel cellular users, which can lead to cellular communication access failures. There are two reasons for cellular communication access failures: (1)D2D interference and (2)insufficient spectrum resources. To address the absence of research on the performance of cellular services' access in D2D underlaid cellular networks, this paper defines the new services' access failure probability and handoff services' access failure probability to evaluate the effect of both D2D interference and limited resources on cellular communication access. Based on the stochastic geometry and stochastic process, a random network model is presented to estimate the access failure probabilities, which can provide guidelines for network design to ensure cellular services' access. The accuracy of the estimated access failure probability is validated through extensive simulations.     

打车软件混合随机均衡模型时间可靠性研究*

为了探究打车软件出现后对乘客打车行为的影响,揭示是否使用打车软件对乘客候车时间长短的变化规律,基于路网混合随机均衡模型理论,在考虑打车软件对出租车司机搜索行为影响和随机变化的OD对需求条件下,构建基于弹性需求的打车软件随机用户均衡模型;然后结合乘客等车、司机空驶时间和可靠性计算模型,引入连续平均（MSA）算法和随机路径流量分配（Dial）算法进行求解;最后通过算例验证了所建模型和算法的有效性。研究结果表明不同需求弹性下、是否使用打车软件对会乘客候车时间及候车时间可靠性产生明显的差异。     

基于T-S模型的随机双线性系统的稳定问题

主要研究了基于T-S模型的随机双线性系统的稳定性问题。首先,利用并行分布补偿方法设计控制器,确保闭环系统是随机渐近稳定的。其次,基于It^o随机稳定性理论,利用Lyapunov函数方法、不等式变换技巧和Schur补引理,证明了定理所给的稳定条件下的结论是成立的。设计方法的有效性通过一个数值例子来验证。     

基于随机共振原理的低频弱信号检测方法研究

介绍了双稳系统,讨论了产生随机共振的条件以及输出频谱的特性。针对原双稳系统不能检测中低频率信号的问题,利用参数变换原理,推导出了一种新的模型,阐述与分析了该模型的参数变化对输出混合信号的影响。模型相对于经典双稳系统模型降低了对输入的要求。     

Methodology for estimating probability of dynamical system’s failure for concrete gravity dam简

Methodology for the reliability analysis of hydraulic gravity dam is the key technology in current hydropower construction.Reliability analysis for the dynamical dam safety should be divided into two phases：failure mode identification and the calculation of the failure probability.Both of them are studied based on the mathematical statistics and structure reliability theory considering two kinds of uncertainty characters（earthquake variability and material randomness）.Firstly,failure mode identification method is established based on the dynamical limit state system and verified through example of Koyna Dam so that the statistical law of progressive failure process in dam body are revealed; Secondly,for the calculation of the failure probability,mathematical model and formula are established according to the characteristics of gravity dam,which include three levels,that is element failure,path failure and system failure.A case study is presented to show the practical application of theoretical method and results of these methods.     

一类随机积分-微分方程的均方渐近概周期解

随机微分方程是在解决某些具有随机现象建立起来的一类方程,其中随机微分方程的均方渐近概周期解相比于均方概周期解应用更加广泛.为了研究均方渐近概周期过程在随机微分方程中的应用,利用均方渐近概周期函数的相关性质以及Banach不动点原理讨论了一类随机积分-微分方程均方渐近概周期解的存在性和唯一性.     

Probabilistic Bit Stream Neural Chip: Theory

A design for a neural network chip is proposed using probabilistic bit streams to represent real values. This paper analyzes the performance of the proposed neurons in this design and demonstrates that very simple operations can be used to obtain the desired functionality. It is also shown that a suitable ‘activation function’ for neurons of this type can be obtained using the interaction of two probability distributions. Finally, the paper introduces a variant of the back-propagation learning algorithm which involves computing the derivatives of the output with respect to individual weights in a network of such units.     

A tree approach to options pricing under regime-switching jump diffusion models

A simple, efficient tree is developed to price options in a very general regime-switching jump diffusion model. Under this model, the switching rates of the switching process depend on the underlying stock price process. Sufficient conditions that guarantee the positivity of branch probabilities are provided. Using the regime-switching tree, we approximate Heston's stochastic volatility model with an additional jump component. Finally, we illustrate the effectiveness of the tree method by several numerical examples.