Optimal time delays in a class of reaction-diffusion equations

ABSTRACT

A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the associated solution of the delay equation is the best approximation of a desired state function. The differentiability of the mapping is proved that associates the solution of the delay equation to the vector of weights and delays. Based on an adjoint calculus, first-order necessary optimality conditions are derived. Numerical test examples show the applicability of the concept of optimizing time delays.     

基于EKF的水下LD通信精对准控制算法

高速激光通信中接收机与光斑中心很难处于精对准状态,导致水下光通信链路难以稳定建立.首先采用蒙特卡洛仿真统计法分析激光光子在海水中传输的接收光强分布规律,再通过实验对接收端的光斑图像进行采样分析,利用曲线拟合得到接收器位置与接收光强的关系.仿真与实验结果表明:光束经过25 m的水下传输,接收光强分布仍近似为高斯分布.采用非线性估计算法(扩展卡尔曼滤波)与基本状态控制反馈理论,根据接收光强度估计接收器当前位置与最大光强处的距离,通过反馈算法实现接收端与光斑中心的主动跟踪对准.算法仿真结果显示,接收端对准误差在2 mm以下,稳定后接收效率超过98%.     

Time reversal acoustic communication receivers: DSP implementation and fast channel estimation

A communication system is implemented on digital signal processors (DSPs) for the underwater acoustic environment. The implemented receiver uses time reversal multi-channel combining followed by a single-channel decision feedback equalizer. Periodic channel estimation is employed to track the channel fluctuations. These techniques are used to mitigate time-varying inter-symbol interference, which is the main challenge in the underwater acoustic channel at operating frequencies greater than 10 kHz. Various optimization tasks are performed to reduce the receiver computational complexity. A fast implementation of the matching pursuit algorithm is tested on the DSP platform. Its performance, in terms of accuracy and run-time, is compared with that of the basic matching pursuit algorithm. Experimental results of the transmission and demodulation of binary phase-shift keying signals at three different symbol rates were obtained in the local Delaware Bay. The low bit error rates demonstrate the effectiveness of our implementation.     

D-admissible hybrid control of a class of singular systems

This paper mainly studies the problem of designing a hybrid state feedback D-admissible controller for a class of linear and nonlinear singular systems. Based on the relationship between singular discrete systems and singular delta operator systems, several necessary and sufficient conditions for a linear singular delta operator system to be D-admissible (i.e. regular, causal and all finite poles lie in a prescribed circular region) with different representations are derived. Then, the existence conditions and explicit expressions of a desirable D-admissible controller are given by means of matrix inequalities and strict linear matrix inequalities, respectively. We further extend the obtained results to singular delta operator systems with Lipschitz nonlinear perturbations, and the design methods of hybrid controller are presented for the nonlinear case as well. Finally, numerical examples as well as simulations are provided to illustrate the effectiveness of the theoretical outcomes obtained in the paper.     

Dynamic output feedback consensus of continuous‐time networked multiagent systems

This article addresses the dynamic output feedback consensus problem of continuous‐time networked multiagent systems. Both a fixed topology and Markovian switching topologies are considered. The consensus algorithms are on the base of the output information of each agent's itself and its neighbors. Some sufficient conditions for consensus of multiagent systems are obtained in forms of bilinear matrix inequalities. The algorithm based on the homotopy continuation method is given to compute the feasible controller gains. Numerical simulations are given to show the effectiveness of the proposed results. © 2014 Wiley Periodicals, Inc. Complexity 20: 35–42, 2015     

Uniform stabilization to equilibrium of a nonlinear fluid–structure interaction model

We consider uniform stability to a nontrivial equilibrium of a nonlinear fluid–structure interaction (FSI) defined on a two or three dimensional bounded domain. Stabilization is achieved via boundary and/or interior feedback controls implemented on both the fluid and the structure. The interior damping on the fluid combining with the viscosity effect stabilizes the dynamics of fluid. However, this dissipation propagated from the fluid alone is not sufficient to drive uniformly to equilibrium the entire coupled system. Therefore, additional interior damping on the wave component or boundary porous like damping on the interface is considered. A geometric condition on the interface is needed if only boundary damping on the wave is active. The main technical difficulty is the mismatch of regularity of hyperbolic and parabolic component of the coupled system. This is overcome by considering special multipliers constructed from Stokes solvers. The uniform stabilization result obtained in this article is global for the fully coupled FSI model.     

Generation of sub‐terahertz repetition rates from a monolithic self‐mode‐locked laser coupled with an external Fabry‐Perot cavity

A novel scheme to multiply the repetition rate of a monolithic self‐mode‐locked laser for generating sub‐terahertz pulse sources is successfully demonstrated. A coated Yb:KGW crystal is designed to achieve a self‐mode‐locked operation at a repetition rate of 24 GHz with an average output power exceeding 1.0 W at a pump power of 4.8 W. A partially reflective mirror is utilized to combine with the output surface of the gain medium to constitute an external Fabry‐Perot cavity. It is theoretically and experimentally verified that adjusting the external cavity length to satisfy the commensurate condition can lead to the frequency spacing to be various order harmonics of the mode spacing of the monolithic cavity. The maximum pulse repetition rate of the laser output can be up to 216 GHz and the pulse duration is as short as 330 fs. More importantly, the overall characteristics of the first‐order temporal autocorrelation traces obtained by sequentially scanning the external cavity.length display an intriguing phenomenon of temporally fractional revivals, similar to the feature of spatial Talbot revivals.

     

基于毕业学生的信息追踪与反馈机制提高教学管理效率与人才培养质量

学生是教育的受体,学生的意见在推进课程建设、教学改革以及提升人才培养质量等方面具有重要的指导和借鉴意义。秉承立德树人的理念,以服务学生成长发展为核心,育人成果为导向,探讨做好教育的实施主体和接受主体之间互相反馈的机制和模式,对不断推动教学改革向高效率和高质量方向发展具有重要意义。着重探讨了化学学院做好毕业生信息追踪的具体路径和意见反馈模式。     

重视反馈的逆向教学设计:以质谱课程的教学为例*

基于逆向教学设计的特点及实践,分析了传统逆向教学设计的课堂实现中存在的关于预期评估与实际评估脱节的问题,阐述了教学反馈的重要性。从而提出了一种重视反馈的逆向教学设计方法。这种方法将评估预判和反馈策略充分结合到逆向教学设计中,在评估和反馈之间进行了有效关联,很好地解决了以上问题。结合笔者在质谱课程中的实践经验,对相应的教学设计的过程进行了举例说明。