统一混沌系统的脉冲鲁棒镇定

对统一混沌系统的鲁棒镇定问题进行了分析，采用脉冲控制方法对该类系统进行控制，利用Lyapunov函数得出受不确定扰动的统一混沌系统鲁棒镇定的充分条件，并且用数值仿真说明得到的充分条件是有效的。     

一种基于小数据量的快速识别短时交通流混沌特性的方法

对短时交通流进行预测、诱导和控制是智能交通控制系统的重要研究内容。由于对短时交通流进行混沌特性识别时,存在实时性与样本数量之间的矛盾。因此,本文基于混沌时间序列分析理论,提出了一种快速计算短时交通流时间序列最大Lyapunov指数的小数据量方法,用于识别短时交通流中是否存在混沌特性。该方法首先将短时交通流时间序列在相空间中进行重构,以充分提取短时交通流中的相关信息。并结合庞卡来截面法对识别结果进行了验证。从而为对短时交通流进行分析、预测和控制时所采用的相应方法提供了可靠的理论依据。对实测短时交通流行为进行识别的结果表明,该方法具有计算量小、实时性好,对小数据量可靠且容易操作等优点。     

Stability analysis of a nonlinear vehicle model in plane motion using the concept of Lyapunov exponents

For the first time, this paper investigates the application of the concept of Lyapunov exponents to the stability analysis of the nonlinear vehicle model in plane motion with two degrees of freedom. The nonlinearity of the model comes from the third-order polynomial expression between the lateral forces on the tyres and the tyre slip angles. Comprehensive studies on both system and structural stability analyses of the vehicle model are presented. The system stability analysis includes the stability, lateral stability region, and effects of driving conditions on the lateral stability region of the vehicle model in the state space. In the structural stability analysis, the ranges of driving conditions in which the stability of the vehicle model is guaranteed are given. Moreover, through examples, the largest Lyapunov exponent is suggested as an indicator of the convergence rate in which the disturbed vehicle model returns to its stable fixed point.     

具有量化误差反馈的车辆纵向跟随控制

针对自动跟随车辆间信息传输存在无线网络量化误差的情况,研究了车辆跟随系统的纵向控制问题.假定每个跟随车辆能够通过无线网络获得相邻车辆及领头车辆的状态信息,并且信息在对数量化器传输下存在量化误差.基于车辆非线性纵向动力学耦合模型和车辆固定间隔跟随策略,应用向量Lyapunov函数方法得出的指数稳定性判据,将量化误差处理为系统状态的不确定性,给出补偿量化误差的滑模控制律,并设计满足系统群稳定性的控制器参数.仿真结果表明:相较于不考虑量化误差的控制器,本控制器能够显著提高车辆跟随误差的收敛速度,确保了自动车辆纵向跟随系统的稳定性.     

欠驱动AUV水平面运动的镇定控制设计

通过对欠驱动AUV的水平面三自由度运动方程和轨迹方程的简化分析,设计了一种镇定控制律。基于全局微分同胚坐标变换将欠驱动AUV的数学模型转化为级联形式的非线性系统,并证明了原系统的镇定问题可简化为级联子系统的镇定问题。通过状态反馈控制研究得到镇定控制律,证明了控制律的收敛性,并且进行了镇定仿真实验演示。仿真结果表明控制律的有效性,能够在任意初始条件下实现镇定控制。     

综合混沌相空间重构与相似性原理的铁路客流量预测

重构相空间理论对我国铁路客流量数据时间序列进行相空间重构,通过计算分形维数和提取最大Lyapunov指数,分析得出了铁路客流量时间序列数据的演化具有混沌特征,结合我国铁路客流量在全年中的波动特点,提出适合我国国情的综合混沌相空间重构与相似性原理的铁路客流量预测算法.该算法能自动参考过去相似年度同期的客流量变化趋势,对预测值进行智能化调整.通过以某火车站客流量为预测对象进行验证,结果证明了该预测算法的准确性和实用性.     

Feedback control strategy of a new car-following model based on reducing traffic accident rates

ABSTRACT

To reduce the traffic accident death rate effectively and alleviate the traffic congestion phenomenon, this study proposes a new type of car-following model under the influence of drivers’ time-varying delay response time. Based on Lyapunov function theory, this paper reduces the traffic accident rate problem to the stability issues of the new model. By constructing suitable Lyapunov functions and using the linear matrix inequality method, the stability problem of the new car-following model is studied. The model, under the action of the controller, can effectively restrain traffic congestion. Using the traffic accident rate model proposed by Solomon, compared with the car-following model without the controller, the model under the controller shows a stronger convergence. This also means that the traffic congestion phenomenon has been effectively suppressed while greatly reducing the mortality rate of traffic accidents.     

带脉冲和时滞的二阶微分方程的稳定性

研究了带脉冲和时滞的二阶微分方程的稳定性问题。通过构造合适的Lyapunov函数,利用稳定性理论和脉冲控制方法,证明了对于不稳定的时滞二阶微分方程,可以通过加强一定的脉冲控制使其稳定。获得的结果改进和推广了前人的工作,提供的例子表明了获得结果的有效性。     

Robust stability of neutral systems: A discretized Lyapunov functional method

This paper focuses on the robust stability for time-delay systems of neutral type. A new complete Lyapunov-Krasovskii function (LKF) is developed. Based on this function and discretization, stability conditions in terms of linear matrix inequalities are obtained. A class of time-varying uncertainty of system matrices can be studied by the method. Foundation item: the National High Technology Research and Development Program (863) of China (No. 2006AA05Z148)