Global smooth solutions for semilinear Schrödinger equations with boundary feedback on 2-dimensional Riemannian manifolds

This paper considers the existence of global smooth solutions of semilinear schrödinger equation with a boundary feedback on 2-dimensional Riemannian manifolds when initial data are small. The authors show that the existence of global solutions depends not only on the boundary feedback, but also on a Riemannian metric, given by the coefficient of the principle part and the original metric of the manifold. In particular, the authers prove that the energy of the system decays exponentially.     

An augmented BV setting for feedback switching control

<正> This paper considers dynamical systems under feedback with control actions limited toswitching.The authors wish to understand the closed-loop systems as approximating multi-scale problemsin which the implementation of switching merely acts on a fast scale.Such hybrid dynamicalsystems are extensively studied in the literature,but not much so far for feedback with partial stateobservation.This becomes in particular relevant when the dynamical systems are governed by partialdifferential equations.The authors introduce an augmented BV setting which permits recognition ofcertain fast scale effects and give a corresponding well-posedness result for observations with such minimalregularity.As an application for this setting,the authors show existence of solutions for systemsof semilinear hyperbolic equations under such feedback with pointwise observations.     

网络型耦合复动力系统的同步动力学

通过讨论网络型耦合复动力系统的同步动力学问题,给出了该系统同步流形稳定性的分析方法,得到了网络型耦合复动力系统局部同步和全局同步的充分条件。所得的结果可以应用到由一个典型的复洛伦兹系统构成的网络耦合复动力系统,数值仿真表明理论结果的正确性。     

Natural Gradient Approach to Multichannel Blind Deconvolution

1.INTroDUCTIOnRecently,theblindseparationofindependentsourceshavebecomeanincreasingimportalresearchareaduetoitssimilaritytotheseparationfeatureinhumanbrain,aswellasitsrapidlygrowingapplicationsinvariousfields,suchastelecommunicationsystems,adageenhancementandbiomedicalsignalprocessing[4,if].Ithasbeenshownthatthenaturalgradientdisprovesdramaticallytheleadingefficiencyininstalltaneousblindseparationandblinddeconvolution.Forthedoublyindnitefiltermixture,thenaturalgradientalgorithmhasbeendevelo…     

Uncoupled PID Control of Coupled Multi-Agent Nonlinear Uncertain systems

In this paper, PID (proportional-integral-derivative) controllers will be designed to solve the tracking problem for a class of coupled multi-agent systems, where each agent is described by a second-order high-dimensional nonlinear uncertain dynamical system, which only has access to its own tracking error information and does not need to communicate with others. This paper will show that a 3-dimensional manifold can be constructed based on the information about the Lipschitz constants of the system nonlinear dynamics, such that whenever the three parameters of each PID controller are chosen from the manifold, the whole multi-agent system can be stabilized globally and the tracking error of each agent approaches to zero asymptotically. For a class of coupled first-order multi-agent nonlinear uncertain systems, a PI controller will be designed to stabilize the whole system.     

大型复杂人机系统结构、过程建模与组织设计方法研究现状与展望

大型复杂人机系统是人类组织与人工系统构成的开放、动态、复杂的有机整体.本文分析了大型复杂人机系统研究的背景及意义,从结构、过程和组织三个视角总结了相关领域的研究进展,对未来大型复杂人机系统结构、过程建模与组织设计方法的主要研究方向及关键科学问题进行了展望.     

Further results on limitations of sampled-data feedback

To control continuous-time uncertain dynamical systems with sampled data-feedback is prevalent today,but the sampling rate is usually not allowed to be arbitrarily fast due to various physical and/or computational constrains.In this paper,the authors examine the limitations of sampled-data feedback control for a class of uncertain systems in continuous-time,with sampling rate not necessary fast enough and with the unknown system structure confined to a set of functions with both linear and nonlinear growth.The limitations of the sampled-data feedback control for the uncertain systems are established quantitatively,which extends the existing related results in the literature.     

常微分方程数值解法在动力天文中的应用

在动力天文中,利用常微数值解法求解运动方程时,通常会出现两个问题——解的定性性质受到歪曲和轨道沿迹误差的严重累积。本文将介绍利用运动本身的一些力学性质作为控制条件,能够有效地解决这些问题,特别是对Hamiltom系统,采用保持辛结构的差分格式——半积分器(Symplectic Imtegrators),有它独特的优点,而且可以将相应的差分格式稍作修改,就可用于小耗散系统,这对动力天文而言也是很重要的。     

Knowledge-Based Multifaceted Modeling Methodology for Open Complex Giant Systems

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Dynamical Criticality: Overview and Open Questions

Systems that exhibit complex behaviours are often found in a particular dynamical condition, poised between order and disorder. This observation is at the core of the so-called criticality hypothesis, which states that systems in a dynamical regime between order and disorder attain the highest level of computational capabilities and achieve an optimal trade-off between robustness and flexibility. Recent results in cellular and evolutionary biology, neuroscience and computer science have revitalised the interest in the criticality hypothesis, emphasising its role as a viable candidate general law in adaptive complex systems. This paper provides an overview of the works on dynamical criticality that are — To the best of our knowledge — Particularly relevant for the criticality hypothesis. The authors review the main contributions concerning dynamics and information processing at the edge of chaos, and illustrate the main achievements in the study of critical dynamics in biological systems.Finally, the authors discuss open questions and propose an agenda for future work.     

SO(3)上的内蕴滑模观测器设计与应用

基于李群的动力学系统建模方法不依赖局部坐标和浸入空间的特性,因而常被用于描述一般力学系统。针对一类基于李群SO(3)描述的力学系统,考虑了实际姿态位形可测但角速度不可测的情况,利用SO(3)上曲率张量、Levi-Civita联络及测地线等内蕴信息,设计了SO(3)上的Super-Twisting内蕴滑模观测器,对实际姿态位形和旋转角速度进行观测,并在其切空间内分析了所设计观测器的收敛性能。最后将所设计的观测器应用在四旋翼平台并进行仿真,仿真结果表明,所设计的观测器具有较好的观测效果和较强的鲁棒性。     

肌肉中的HH模型钠离子通道反电势的Hopf分岔分析

以肌肉中的Hodgkin-Huxley模型为研究对象，研究病理实验中有显著变化的钠离子通道反电势参数对Hodgkin-Huxley模型的影响并分析其Hopf分岔。采用高维方程的代数判据进行Hodgkin-Huxley模型单参数动态分岔分析，简化了分析过程，并用研究结果解释相应的生理过程，试图从生物系统动态过程异变的角度探讨生理疾病的成因。     

IRS与人工噪声辅助的MIMO通信系统物理层安全方案设计

针对多输入多输出通信系统信息传输过程中的安全问题, 提出一种智能反射表面(intelligent reflecting surface, IRS)与人工噪声辅助的物理层安全设计方案。在该方案中, 首先基于系统保密速率最大化准则, 构建一非凸优化问题。由于该问题求解需联合优化设计基站波束赋形矩阵、人工噪声协方差矩阵及IRS相移矩阵，为易于求解, 基于均方误差准则, 对非凸目标函数进行等价转换。最后, 以交替迭代方式分别利用内点法和基于黎曼流形的共轭梯度下降算法, 求解波束赋形矩阵和人工噪声协方差矩阵以及IRS相移矩阵。仿真结果表明, 所提方案的系统保密速率在发送端具有较高的发送功率时, 优于其他几种方案。     

基于多Agent的地面作战建模仿真研究

计算机作战仿真是军事人员的“作战实验室”。然而,作战系统是一个复杂的非线性动态系统,对其进行建模困难,Agent和多Agent技术为计算机作战仿真提供了新的建模仿真方法。本文首先分析了作战系统的特点和传统的数学建模的不足,其次介绍了有关Agent、多agent系统和多Agent系统仿真的概念,并分析了基于多Agent的建模与传统的数学建模的区别,最后,分析了一个基于Agent建模与仿真技术的陆军地面作战仿真系统。     

液压集成系统智能化虚拟设计中的核心算法研究

通过对液压集成系统设计中存在的问题进行分析,提出以集成块布局布孔集成方案的智能优化设计算法为核心,以具有沉浸感的虚拟现实环境为人机交互界面的智能化虚拟设计新方法。针对集成块这种复杂的立体空间带约束布局问题,介绍了智能型虚拟设计系统的构造方案,重点对其核心算法—运用智能计算方法及其混合优化策略实现集成块布局布孔自动优化设计的方法和实现技术进行阐述,为建造高度智能的液压集成块虚拟设计系统提供了可靠的理论依据。     

基于RBF神经网络的鲁棒滑模观测器设计

针对非线性不确定性系统,提出一种鲁棒滑模观测器。所提出的鲁棒滑模观测器通过滑模与相应的控制策略来实现。设计参数的选取不需要求解大量方程,同时能保证对系统的非线性不确定性具有鲁棒性,系统中不确定性的上界值采用RBF神经网络进行自适应学习。通过设计滑模,可以调整观测器跟踪系统状态的收敛速度,使状态估计达到预期的指标。仿真结果验证了提出方法的有效性。     

Complexity analysis of network-based dynamical systems

This paper investigates the nonlinear dynamics of network-based dynamical systems where network communication channels of finite data rates are inserted into the closed loops of the control systems. The authors analyze the bifurcation and chaotic behavior of the non-smooth dynamical systems. The authors first prove that for almost all system parameters there are no periodic orbits. This result distinguishes this type of non-smooth dynamical systems from many others exhibiting border-collision bifurcations. Next, the authors show analytically that the chaotic sets are separated from the region containing the line segment of all fixed points with a finite distance. Finally, the authors employ a simple model to highlight that both the number of clients sharing a common network channel and fluctuations in the available network bandwidth have significant influence on the performance of such dynamical systems.     

Generating semi-algebraic invariants for non-autonomous polynomial hybrid systems

Hybrid systems are dynamical systems with interacting discrete computation and continuous physical processes, which have become more common, more indispensable, and more complicated in our modern life. Particularly, many of them are safety-critical, and therefore are required to meet a critical safety standard. Invariant generation plays a central role in the verification and synthesis of hybrid systems. In the previous work, the fourth author and his coauthors gave a necessary and sufficient condition for a semi-algebraic set being an invariant of a polynomial autonomous dynamical system, which gave a confirmative answer to the open problem. In addition, based on which a complete algorithm for generating all semi-algebraic invariants of a given polynomial autonomous hybrid system with the given shape was proposed. This paper considers how to extend their work to non-autonomous dynamical and hybrid systems. Non-autonomous dynamical and hybrid systems are with inputs, which are very common in practice; in contrast, autonomous ones are without inputs. Furthermore, the authors present a sound and complete algorithm to verify semi-algebraic invariants for non-autonomous polynomial hybrid systems. Based on which, the authors propose a sound and complete algorithm to generate all invariants with a pre-defined template.     

HARMONIC MAPS VERSUS POISSON EQUATIONS ON NONCOMPACT RIEMANNIAN MANIFOLDS

1.Introducti0llStartingfromtheworkofP.LiandT.F.Taml1'2])therearesomeprogressonthestudyofharmonicmaPsbetweennegativelycurvedc0mplete,noncompactriemannianmanifolds.Wemayquote[2-5]justforafew.Thenewstartingpoilltin[1]isthea-ssumption0fagivenmaPwithitstensi0nfieldinasuitableSob0levspace.Asacomparison,wementi0nthatthekeytechniqueofthemethod0fEells-Sampsonl6]istheuseofaBochnertypeevoluti0n0ftheenergydensitywithaninitialdataoftotalenergy.InthispaPer,wetrytogivealargec1assofapprokimateharmonicma…     

Bidirectionally coupled synchronization of the generalized Lorenz systems

Wu, Chen, and Cai (2007) investigated chaos synchronization of two identical generalized Lorenz systems unidirectionally coupled by a linear state error feedback controller. However, bidirectional coupling in real life such as complex dynamical networks is more universal. This paper provides a unified method for analyzing chaos synchronization of two bidirectionally coupled generalized Lorenz systems. Some sufficient synchronization conditions for some special coupling matrices (diagonal matrices, so-called dislocated coupling matrices, and so on) are derived through rigorously mathematical theory. In particular, for the classical Lorenz system, the authors obtain synchronization criteria which only depend upon its parameters using new estimation of the ultimate bounds of Lorenz system (Chaos, Solitons, and Fractals, 2005). The criteria are then applied to four typical generalized Lorenz systems in the numerical simulations for verification.