Analysis of finite-time practical stability for time-varying polytopic systems

The problem of finite-time practical stability (FTPS) for time-varying polytopic systems is discussed. Three equivalent conditions for FTPS are first proposed. To facilitate the system analysis, a sufficient linear matrix inequality (LMI) criterion on the FTPS is further provided. The definition of finite-time practical boundedness and a sufficient LMI criterion are also provided to overcome the exogenous disturbance. A numerical example is used to illustrate the effect of the proposed approach.     

Tracking controller for robot manipulators via composite nonlinear feedback law

A composite nonlinear feedback tracking controller for motion control of robot manipulators is de-scribed. The structure of the controller is composed of a composite nonlinear feedback law plus full robot nonlinear dynamics compensation. The stability is carried out in the presence of friction. The controller takes advantage of varying damping ratios induced by the composite nonlinear feedback control, so the transient performance of the closed-loop is remarkably improved. Simulation results demonstrate the feasibility of the proposed method.     

Improved hybrid position/force controller design of a flexible robot manipulator using a sliding observer

An improved hybrid position/force controller design of a flexible robot manipulator is presented using a sliding observer. The friction between the end effector and the environment is considered and compensated. For systematic reasons the controller is designed taking into consideration the rigid link subsystems and the flexible joints. The proposed control system satisfies the stability of the two subsystems and copes with the uncertainty of robot dynamics. A sliding observer is designed to estimate the time derivative of the torque applied as input to the rigid part of the robot. For the stability of the observer, it is assumed that the uncertainty of the observed system is bounded. A MRAC algorithm is used for the estimation of the friction forces at the contact point between the end effector and the environment. Finally simulation and experimental results are given, to demonstrate the effectiveness of the proposed controller.     

基于半离散化的中立型时滞系统的数值仿真

中立型时滞系统是现代工程研究中的一个非常普遍的对象,该系统经过降阶近似后可以转换为一个多时滞系统近似求解的问题.提出将半离散化方法拓展到多时滞系统,应用于中立型时滞系统的数值近似求解,并在此基础上分析系统的稳定性,导出其最优控制增益.仿真结果表明,该方法提供了一种有效的求解和设计线性周期性中立型时滞系统的数值手段.     

一种基于奇异值分解的非线性滤波新算法

提出一种基于奇异值分解的无导数卡尔曼非线性滤波新算法对UKF算法进行改进.该算法利用奇异值分解作为工具,将原算法中的协方差矩阵进行奇异值分解,可以在一定程度上避免在递推过程中,由于计算误差和舍入误差而引起的协方差矩阵失去正定性,从而导致算法失效的问题.在不降低滤波精度,不增加算法复杂度的前提下,新算法具有很好的数值稳定性.实例仿真结果验证了本方法的有效性.     

羊群行为加剧股票价格波动吗?

羊群行为是否加剧股票价格波动,已有研究甚至给出截然相反的结论.假定交易者买卖观点的转变主要受其对股票基础价值认知和其他交易者行为的影响,本文构建描述市场平均投资态度和股票价格变化的数学模型,利用离散动力系统的相关理论研究模型的稳定性,并根据金融市场稳定与否对羊群行为程度进行界定.研究结果表明,在轻度羊群效应区间内,股票价格相应地呈现微幅周期波动;在中度羊群效应区间内,股票价格在经历一段时间的阻尼式波动后收敛至均衡价格,并且在此区间中存在最优的羊群行为,它促使股票价格以最快的速度逼近均衡价格;而在重度羊群效应区间,股票价格发生大幅的非理性波动,可以导致股市严重泡沫和金融危机的产生.     

可再生资源可持续发展的动力学模型分析

以《资源—经济可持续发展的最优经济发展模型》中模型的动态方程为基础,重点研究资源的恢复性投资对可再生资源的可持续利用的影响,应用非线性动力学方法研究了系统正不动点的存在性、局部稳定性,然后用数值模拟的方法验证了正不动点的局部稳定性,最后应用全局分析方法给出了维持资源可再生能力的当前资源存量范围(可行吸引域)。     

An Analysis of an SIRS Epidemic Model with General Direct Immunization in Networks北大核心CSCD

We consider an SIRS epidemic model with a general direct immunization rate on networks. By constructing suitable Lyapunov functions, we find that the dynamical behvaior of the model is completely determined by the epidemic threshold λc. When λ≤λc, the disease-free equilibrium is globally asymptotically stable; when λ>λc, the endemic equilibrium is globally asymptotically stable. In addition, we propose a uniform direct immunization and a targeted direct immunization. The results show that under the same average immunization rate s there exists a critical immunization-lost rate δc so that the epidemic threshold of the targeted direct immunization is smaller (larger) than that of the uniform direct immunization if δ<δc(δ>δc). © 2017, The Journal of Agency of Complex Systems and Complexity Science. All right reserved.     

基于分离设计/集成优化的机器人步态规划

针对双足机器人步行问题，提出了一种基于分离设计／集成优化的步态规划方法。基于双足机器人的步行特征，实施多时空和多关节的任务分离，进而实现多时空关节的步态分离规划。进一步基于零力矩点理论，提出了一种综合机构修正和步态修正方法的步态规划集成优化策略。这种基于分离设计／集成优化的步态规划策略极大简化了复杂多关节双足机器人的规划过程，仿真研究表明了该方法的有效性。     

多模型自适应控制算法的性能分析

多模型自适应控制利用多个元素模型覆盖被控对象的不确定性,并针对这多个元素模型建立多个稳定的控制器。每一个采样时刻,基于一个以模型输出误差为变量的具有积分特点的指标切换函数,选择描述被控对象最优的元素模型,并将基于此模型的控制器切换为当前被控对象的控制器。研究如何调整多模型自适应控制器的结构和参数,提高控制品质,为多模型自适应控制器的应用和进一步研究提供理论基础。