达布定理的一个应用

应用达布定理,纠正了不定积分计算中的一个错误。     

Robust hierarchical controller with conditional integrator based on small gain theorem for reference trajectory tracking of autonomous vehicles

ABSTRACT

A robust trajectory tracking controller is designed for autonomous vehicles based on a hierarchical architecture to make the autonomous vehicle track a given reference trajectory. The controller consists of two sub controllers: kinematic controller and dynamic controller. Based on the kinematics of tracking reference trajectory, a desired yaw rate is calculated by kinematic controller to make the lateral deviation global asymptotic stable. Then, steering wheel angle is calculated by a vehicle dynamic controller to make the vehicle yaw rate converge to the desired value and make the vehicle dynamic stable. Conditional integration method is used in the sub controllers. This method guarantees global asymptotic stability of tracking reference values and considers the uncertainty of parameters and constraints of desired yaw rate and actuators. Then based on small-gain theorem, the condition of the finite-gain L stability is given to the hierarchical controller to ensure the interconnected sub systems stable and prevent the amplification of system disturbance. Finally, the effectiveness and robustness of the controller are validated by real vehicle experiments.     

Development of a systematic and practical methodology for the design of vehicles semi-active suspension control system

In this paper, a novel systematic and practical methodology is presented for design of vehicle semi-active suspension systems. Typically, the semi-active control strategies developed to improve vehicle ride comfort and stability have a switching nature. This makes the design of the controlled suspension systems difficult and highly dependent on an extensive trial-and-error process. The proposed methodology maps the discontinuous control system model to a continuous linear region, where all the time and frequency design techniques, established in the conventional control system theory, can be applied. If the semi-active control system is designed to satisfy some ride and stability requirements, an inverse mapping offers the ultimate control law. At the end, the entire design procedure is summarised in six steps. The effectiveness of the proposed methodology in the design of a semi-active suspension system for a Cadillac SRX 2005 is demonstrated with road tests results. Real-time experiments confirm that the use of the newly developed systematic design method reduces the required time and effort in real industrial problems.     

一类奇异泛函微分方程边值问题的正解

利用锥拉伸与锥压缩不动点理论讨论了一类具有限时滞二阶奇异泛函微分方程三点边值问题正解的存在性,建立了一类奇异泛函微分方程边值问题至少存在一个正解的充分性条件并推广和改进了已有的结果.     

一类含有时滞的脉冲微分方程的正周期解

研究了一类含有时滞的脉冲微分方程,在系数变号的情形下,利用锥上的不动点定理获得了其正ω-周期解的存在性结果.     

管棚预支护条件下水下隧道开挖面三维稳定性分析

基于塑性极限分析理论,建立了考虑渗流力的管棚预支护条件下隧道开挖面三维稳定性分析模型,由此确定开挖面的极限支护压力。结合深圳地铁实际工程,采用该方法计算得到的开挖面极限支护压力与流固耦合数值计算结果吻合较好,验证了该方法的合理性,进而研究了管棚预支护对隧道开挖面渗流力的影响,分析了地下水位和管棚剩余长度与开挖面渗流力的关系。分析结果表明:渗流力对隧道开挖面稳定性有显著的影响,而且渗流力与地下水位呈线性关系,当隧道在富水地层施工时,必须考虑渗流力对隧道开挖面稳定性的影响;采用管棚预支护可以显著地减小隧道开挖面处的渗流力,但当开挖面前方管棚剩余长度超过2倍洞径时,再增加管棚长度对减小开挖面渗流力的效果不明显。     

地震效应下二级边坡三维动态稳定性上限分析

为了给二级边坡的抗震设计提供参考,对其在地震力作用下的稳定性进行研究。基于三维破坏模型,采用拟静力法将地震力引入计算模型中,运用极限分析上限定理分析二级边坡破坏时的能量耗散,并根据虚功率原理推导稳定系数的解析解。利用穷举法优化计算,得到约束条件下稳定系数的最优上限解,并与已有研究成果进行对比。利用该方法,分析宽高比、内摩擦角、深度系数、上、下台阶倾角、地震力等因素对二级边坡稳定性的影响。针对不同的计算精度,给出二级边坡可简化为二维平面应变问题的最小宽高比。研究结果表明：该方法正确可靠;宽高比对稳定系数影响显著,随着宽高比的增大,二级边坡的三维效应逐渐弱化,最终转变为二维平面应变问题,内摩擦角、深度系数、上、下台阶倾角对稳定系数有较大影响;对边坡进行放坡时,应尽量减小上、下台阶的倾角,并增大上台阶边坡的高度,以提高二级边坡的稳定性;水平地震力与竖直地震力对二级边坡的稳定性有显著影响,如果计算中不考虑地震力,则稳定系数的相对误差分别高达40%和15%。     

Radon-Nikodym定理的两种证明方式的比较

笔者在本文讨论应用Riesz-Frechet定理证明R-N定理.拟定的证明改进了文[1]中给出的简略证明,且在问题的处理方面与文[1]的论述略有不同.R-N定理的两种证明方式各有其独特之处.这两种证法都值得研究.     

Solution and Positive Solution to Nonlinear Cantilever Beam Equations

Using the decomposition technique of equation and the fixed point theorem, the existence of solution and positive solution is studied for a nonlinear cantilever beam equation. The equation describes the deformation of the elastic beam with a fixed end and a free end. The main results show that the equation has at least one solution or positive solution, provided that the ＂height＂ of nonlinear term is appropriate on a bounded set.     

Generalized S-KKM Theorems and Minimax Inequalities in FC-Spaces

The concept of FC-closed subset in FC-spaee without any linear structure was introduced. Then, the generalized KKM theorem is proved for FC-closed value mappings under some conditions. The FC-space in the theorem is the generalization of L-convex space and the condition of the mapping with finitely FC-closed value is weaker than that with finitely L-closed value.