High-order adaptive Gegenbauer integral spectral element method for solving non-linear optimal control problems

In this work, we propose an adaptive spectral element algorithm for solving non-linear optimal control problems. The method employs orthogonal collocation at the shifted Gegenbauer–Gauss points combined with very accurate and stable numerical quadratures to fully discretize the multiple-phase integral form of the optimal control problem. The proposed algorithm relies on exploiting the underlying smoothness properties of the solutions for computing approximate solutions efficiently. In particular, the method brackets discontinuities and ‘points of nonsmoothness’ through a novel local adaptive algorithm, which achieves a desired accuracy on the discrete dynamical system equations by adjusting both the mesh size and the degree of the approximating polynomials. A rigorous error analysis of the developed numerical quadratures is presented. Finally, the efficiency of the proposed method is demonstrated on three test examples from the open literature.     

Hopf bifurcation and chaos control in a new chaotic system via hybrid control strategy

In this paper, we investigate the problem of Hopf bifurcation and chaos control in a new chaotic system. A hybrid control strategy using both state feedback and parameter control is proposed. Theoretical analysis shows that the Hopf bifurcation critical value can be changed via hybrid control. Meanwhile, this control strategy can also control the chaos state. The direction and stability of bifurcating periodic solutions are determined by the normal form theory and the center manifold theorem. Finally, numerical simulations are carried out to illustrate the effectiveness of the main theoretical results.     

无标度复杂网络负载传输优化策略

提出了一种能够显著提高无标度复杂网络负载传输性能的优化路由策略.实现了负载在核心节点与边缘节点间的合理分配.分析表明该策略使得网络的负载处理能力正比于网络规模的平方,而与单个节点的度值无关.实验结果显示优化路由策略在保持了最短路由策略小世界效应的同时,成倍地提升了网络的负载传输能力,且随着网络平均节点度的增加其优势越趋显著.此外,与有效路由策略的比较进一步验证了优化路由策略的优异性能. 关键词： 优化路由策略 复杂网络 负载传输 网络阻塞     

Multi-step-prediction of chaotic time series based on co-evolutionary recurrent neural network

This paper proposes a co-evolutionary recurrent neural network （CERNN） for the multi-step-prediction of chaotic time series, it estimates the proper parameters of phase space reconstruction and optimizes the structure of recurrent neural networks by coevolutionary strategy. The searching space was separated into two subspaces and the individuals are trained in a parallel computational procedure. It can dynamically combine the embedding method with the capability of recurrent neural network to incorporate past experience due to internal recurrence. The effectiveness of CERNN is evaluated by using three benchmark chaotic time series data sets： the Lorenz series, Mackey-Glass series and real-world sun spot series. The simulation results show that CERNN improves the performances of multi-step-prediction of chaotic time series.     

量子博弈论及其应用

介绍了量子博弈理论及与经典博弈理论的关系，指出了量子博弈理论的优越性，及对现实物理世界的意义。     

Quantum Game with Restricted Matrix Strategies

We study a quantum game played by two players with restricted multiple strategies. It is found that in this restricted quantum game Nash equilibrium does not always exist when the initial state is entangled. At the same time,we find that when Nash equilibrium exists the payoff function is usually different from that in the classical counterpart except in some special cases. This presents an explicit example showing quantum game and classical game may differ.When designing a quantum game with limited strategies, the allowed strategy should be carefully chosen according to the type of initial state.     

基于多信号流模型的诊断策略动态生成

针对静态故障树诊断序列长、人工可干预度差和不支持多现象并行推理问题,提出了基于D-矩阵和Rollout信息启发搜索算法的故障诊断策略动态生成方法,介绍了基于TEAMS多信号流模型的D-矩阵数据获取方法和Rollout信息启发搜索算法的DLL独立封装技术、输入输出数据规范和动态交互控制方法;基于此开发的交互式智能诊断系统(IIDS)软件平台经实际现场测试诊断验证,对诊断现场出现的多种客观条件,如系统工作模式或测试资源变化、用户干预和多故障现象并发推理等具有很好的适应性,故障覆盖率和隔离率指标高,对提高装备故障诊断的效率、准确性和灵活性具有显著作用。     

Design of triangular FBG filter for sensor applications using covariance matrix adapted evolution algorithm

The design of triangular fiber Bragg grating (TFBG) filters using covariance matrix adapted evolution strategy (CMAES) algorithm is presented. The TFBG filter can be used as a readout device in FBG-based sensor applications. Two different filter design problems are investigated. The first problem is the design of TFBG filter for a specified bandwidth. The other is maximizing the bandwidth of the TFBG filter for a given grating length and maximum index modulation of the FBG. A more practical asymmetrical triangular FBG filter design is also considered. The results show that for the same grating length and maximum index modulation, a larger bandwidth can be achieved with a chirped grating. The maximized bandwidth design can be used to achieve the maximum possible bandwidth for the specified grating length, maximum index modulation and chirp rate. The results obtained using CMAES algorithm (codes available at http://www.ntu.edu.sg/home/epnsugan) is compared with the results of PSO and other algorithms. Comparisons show that the CMAES algorithm is more consistent in obtaining the best solution with reduced computation time. Hence, the CMAES algorithm is effective for the design of TFBG filters for sensor applications.     

Mitigation strategies on scale-free networks against cascading failures

According to the dynamic characteristics of the cascading propagation, we introduce a mitigation mechanism and propose four mitigation methods on four types of nodes. By the normalized average avalanche size and a new measure, we demonstrate the efficiencies of the mitigation strategies on enhancing the robustness of scale-free networks against cascading failures and give the order of the effectiveness of the mitigation strategies. Surprisingly, we find that only adopting once mitigation mechanism on a small part of the overload nodes can dramatically improve the robustness of scale-free networks. In addition, we also show by numerical simulations that the optimal mitigation method strongly depends on the total capacities of all nodes in a network and the distribution of the load in the cascading model. Therefore, according to the protection strength for scale-free networks, by the distribution of the load and the protection price of networks, we can reasonably select how many nodes and which mitigation method to efficiently protect scale-free networks at the lower price. These findings may be very useful for avoiding various cascading-failure-induced disasters in the real world and for leading to insights into the mitigation of cascading failures.     

Analysis of network traffic flow dynamics based on gravitational field theory

For further research on the gravity mechanism of the routing protocol in complex networks,we introduce the concept of routing awareness depth,which is represented by ρ.On this basis,we define the calculation formula of the gravity of the transmission route for the packet,and propose a routing strategy based on the gravitational field of the node and the routing awareness depth.In order to characterize the efficiency of the method,we introduce an order parameter,η,to measure the throughput of the network by the critical value of phase transition from free flow to congestion,and use the node betweenness centrality,B,to test the transmission efficiency of the network and congestion distribution.We simulate the network transmission performance under different values of the routing awareness depth,ρ.Simulation results show that if the value of the routing awareness depth ρ is too small,then the gravity of the route is composed of the attraction of very few nodes on the route,which cannot improve the capacity of the network effectively.If the value of the routing awareness depth ρ is greater than the network's average distance l,then the capacity of the network may be improved greatly and no longer change with the sustainable increment of routing awareness depth ρ,and the routing strategy performance enters into a constant state.Moreover,whatever the value of the routing awareness depth ρ,our algorithm always effectively balances the distribution of the betweenness centrality and realizes equal distribution of the network load.