带离散不等式约束的LQ最优控制

在笔者文[1]中,我们给出了一类实抽象Hilbert空间中对状态变量x和控制变量u带有线性等式约束或带有凸约束并具有二次型代价指标的有限时域线性控制过程最优解(x~*,u~*)的存在唯一性定理及特征性定理,证明了两类约束条件下的最优解分别是Hilbert空间中插值样条函数和凸集上的样条函数。在笔者的文[2]中,又对实Hilbert函     

Undetermination of the relation between network synchronizability and betweenness centrality

Betweenness centrality is taken as a sensible indicator of the synchronizability of complex networks. To test whether betweenness centrality is a proper measure of the synchronizability in specific realizations of random networks,this paper adds edges to the networks and then evaluates the changes of betweenness centrality and network synchronizability. It finds that the two quantities vary independently.     

Pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions

This paper studies pinning-controlled synchronization of complex networks with bounded or unbounded synchronized regions. To study a state-feedback pinning-controlled network with N nodes, it first converts the controlled network to an extended network of N+1 nodes without controls. It is shown that the controlled synchronizability of the given network is determined by the real part of the smallest nonzero eigenvalue of the coupling matrix of its extended network when the synchronized region is unbounded; but it is determined by the ratio of the real parts of the largest and the smallest nonzero eigenvalues of the coupling matrix when the synchronized region is bounded. Both theoretical analysis and numerical simulation show that the portion of controlled nodes has no critical values when the synchronized region is unbounded, but it has a critical value when the synchronized region is bounded. In the former case, therefore, it is possible to control the network to achieve synchronization by pinning only one node. In the latter case, the network can achieve controlled synchronization only when the portion of controlled nodes is larger than the critical value.     

束晕-混沌的非线性反馈离散控制

 基于非线性控制方法，提出了一种特殊的非线性反馈函数， 即小波反馈函数，用于离散控制强流质子束的束晕 混沌。控制后质子束的束晕强度因子很快趋于零，束均方根半径、束横向平均发射度等都减至控制前的三分之一稍多, 证明该控制方法切实有效，在工业上具有实用价值。     

Cost and effect of pinning control for network synchronization

The problem of pinning control for the synchronization of complex dynamical networks is discussed in this paper. A cost function of the controlled network is defined by the feedback gain and the coupling strength of the network. An interesting result is that a lower cost is achieved by using the control scheme of pinning nodes with smaller degrees. Some strict mathematical analyses are presented for achieving a lower cost in the synchronization of different star-shaped networks. Numerical simulations on some non-regular complex networks generated by the Barabási--Albert model and various star-shaped networks are performed for verification and illustration.     

Epidemic spreading on networks with vaccination

In this paper, a new susceptible-infected-susceptible (SIS) model on complex networks with imperfect vaccination is proposed. Two types of epidemic spreading patterns (the recovered individuals have or have not immunity) on scale-free networks are discussed. Both theoretical and numerical analyses are presented. The epidemic thresholds related to the vaccination rate, the vaccination-invalid rate and the vaccination success rate on scale-free networks are demonstrated, showing different results from the reported observations. This reveals that whether or not the epidemic can spread over a network under vaccination control is determined not only by the network structure but also by the medicine's effective duration. Moreover, for a given infective rate, the proportion of individuals to vaccinate can be calculated theoretically for the case that the recovered nodes have immunity. Finally, simulated results are presented to show how to control the disease prevalence.     

小波函数反馈法实现对强流束晕混沌的有效控制

提出小波函数反馈控制法,分别实现了在四种不同的初始质子分布情形下对强流质子束的束晕混沌的有效控制.控制后束晕强度因子变为零,束均方根半径、束横向动量平方和的平均值和相对平均发射度比控制前都减少至1/2—1/3.结果表明该方法十分有效,具有应用前景 关键词： 小波函数反馈法 束晕混沌 强流质子束     

状态反馈和参数调整控制离散非线性系统的倍周期分岔和混沌

利用系统的状态反馈和参数调节的方法，有效地实现了离散非线性动力系统的倍周期分岔的延迟控制和混沌吸引子中不稳定周期轨道的控制.同时，通过选择合适的调控参数，可以将系统从一个2n周期轨道控制到2m(m关键词： 状态反馈 参量调节 混沌控制 分岔控制     

A Chaotic Communication Scheme Based on Generalized Synchronization and Hash Functions

A new chaotic communication scheme based on generalized chaotic synchronization (GCS) and hash function transpositions is presented. The communication scheme has nonsymmetric secrete keys and its ability is similar to traditional digital signatures, i.e. a receiver can convince himself whether or not the sender‘s message contents have been modified. As a direct application of the scheme, a GCS system is designed by using Chen‘s chaotic circuit and is studied in some detail. The numerical simulation shows that this Chen GCS system has high security and is fast and reliable for secure lnternet communications.     

Finite-time control of chaotic systems with nonlinear inputs

A finite-time controller is designed for a class of nonlinear systems subject to sector nonlinear inputs. A novel and simple approach is suggested based on the finite-time control principle. The designed sliding-mode controller can drive a chaotic system to track a smooth target signal in a finite time. The chaotic Duffing--Holmes oscillator is used for verification and demonstration.