约束随机线性二次最优控制的研究

本文研究线性终端状态约束下不定随机线性二次最优控制问题.首先利用Lagrange Multiplier 定理得到了存在最优线性状态反馈解的必要条件, 而在加强的条件下也得到了最优控制存在的充分条件. 从某种意义上讲, 以往关于无约束随机线性二次最优控制的一些结果可以看成本文主要定理的推论.     

书目数据库的完整约束

本文讨论了书目数据库的建设及其完整约束。在建立图书馆集成化系统时, 完整约束是一个重要的课题,它是维护书目数据库正确性的重要组成部分。     

双体多驱动小车非完整约束点镇定问题的研究

推导了双体多驱动小车的运动学方程 ,并且给出了标准链式表达式 ,证明了双体车的镇定控制问题 .     

具有完整约束的变质量系统的机械能守恒律

研究具有双面理想完整约束的变质量力学系统的机械能守恒律.首先,利用系统的运动微分方程,获得能量变化方程,并给出机械能守恒律存在的充分必要条件.然后,提出具有守恒律的27种情形.最后,举例说明.     

非完整约束动力系统的离散积分方法

采用了微分-代数方程求解的雷同策略,只在离散区段内满足无约束的积分,而在离散节点处则用约束冲量(Lagrange乘子向量)让轨道发生转折,给出了非完整约束动力系统的离散积分格式.数值例题的效果表明,本文给出的积分算法严格满足节点的非完整约束,具有良好的长时间积分性能.     

灵巧擦窗机器人非完整约束运动学方程及镇定问题的研究

详细推导了带约束连杆的双车体可重构灵巧擦窗机器人运动学方程,并在此基础上研究了整车体运动控制的反馈镇定问题.     

高阶非完整系统的广义Birkhoff表示

通常方法构造的高阶非完整系统的运动微分方程不仅没有完整系统的辛几何结构和Lie代数结构,而且也不具备完整系统的自伴随性质.本文利用降阶方法,将高阶非完整系统变换为一阶动力学系统,并运用Cauchy-Kowalevski定理对其自伴随化,得到一种新的一阶动力学方程组-广义Birkhoff表示,这将为研究高阶非完整系统的若干动力学问题、几何结构、代数结构、几何数值积分以及工程应用提供了一个新的方法.     

基于调和映射的约束纹理映射方法

传统的约束纹理映射方法大都建立在迭代优化的基础上,给出的解多为近似解．为此,提出了一种基于调和映射的约束纹理映射方法,利用该方法可以得到约束纹理映射问题的一个形式化精确解．由于调和映射具有保持映射能量最小的良好性质,因此该方法能够最小化纹理映射的形变;另外,约束的纹理映射是个大交互量的工作,埘映射效果的优化调整非常重要,提出的自适应局部邻域调整方法能够实现映射效果的实时优化．该方法鲁棒并且效率高,实验结果表明利用该方法能够取得良好的绘制效果．     

一种带线性约束的最小生成树聚类方法

提出了一种带线性约束的最小生成树聚类方法,目标是聚合在空间上大致呈线性密集分布的对象.方法的基本过程是,用线性率阈值约束最小生成树打断边的选取,尽可能使每次打断都能割取出一个满足线性率大于该阈值的子树(类),直至所有合适子树都被割取,残余子树则被抛弃.对自构建数据和真实世界中地震数据的聚类实验证明了该方法的有效性和实用性.     

基于非线性映射的约束系统自适应反推控制

针对基于障碍Lyapunov函数的非线性约束系统反推控制中, 控制器结构复杂、约束量初值选取区间小、会引入额外参数等问题, 提出了一种新的基于非线性映射的自适应反推控制方案. 该方法扩大约束量的初值选取区间为整个约束区间, 增加了系统初值选取和控制器设计的便易性. 约束量被映射至实数空间中, 因此映射后的新系统可以直接应用反推法设计控制器, 简化了控制器结构且不会引入额外参数. 证明了映射前后系统具有一致的收敛性, 保证闭环系统所有信号一致有界, 并且跟踪误差渐近收敛于零. 仿真结果进一步验证了本文方法的有效性.     

事件空间离散完整系统的Noether理论

研究差分离散变分原理和事件空间中离散完整系统的Noether理论. 运用差分离散变分方法,通过群的无限小变换,得到了事件空间中离散完整系统的差分离散变分原理,并建立了离散的运动方程. 得到了系统的Noether对称性的判据方程和Noether守恒量的形式以及其存在的条件. 举例说明结果的应用.     

Linear Momentum,Angular Momentum and Analytical Mechanics

The laws of mechanics can be set forth in different equivalent formulations. Frequently, one formulation can be deduced from another. For example, Lagrange's equations can be deduced both from Newton's law and from Hamilton's principle. One task never undertaken to date is that of deducing the principles of linear and angular momentum from a formulation of analytical mechanics. This task is undertaken in the present note in connection with simple nonholonomic systems.     

A new method for solving interval and fuzzy equations: Linear case

A new approach to the solution of interval and fuzzy equations based on the generalized procedure of interval extension called “interval extended zero” method is proposed. The central for the proposed approach is the treatment of the interval zero as an interval centered around zero. It is shown that such proposition is not of heuristic nature, but is the direct consequence of the interval subtraction operation. Some methodological problems concerned with this definition of interval zero are discussed. It is shown that the resulting solution of interval linear equations based on the proposed method may be naturally treated as a fuzzy number. An important advantage of a new method is that it substantially decreases the excess width effect. On the other hand, we show that it can be used as a reliable practical tool for solving linear interval and fuzzy equations as well as the systems of them. The features of the method are illustrated by the example of the solution of the well known Leontief input-output problem in the interval setting.     

Active tension optimal control for WT wheelchair robot by using a novel control law for holonomic or nonholonomic systems

The characteristics of interaction between WT wheelchair robot and stair environments is analyzed and possible patterns of WT wheelchair robot during the stair-climbing process are summarized, with criteria to determine the pattern of the wheelchair robot proposed. Aiming at the complicated mechanism of WT wheelchair robot with holonomic constraints and combining it with the dynamic programming, namely the Hamilton-Jacobi equation, a new control law called active tension optimal control is presented for holonomic or nonholonomic robotic systems, based on which one can make the wheelchair robot with a holonomic or nonholonomic mechanism track the expected reference input of constraint forces of holonomic or nonholinomic constraints as well as track the expected reference input of the generalized coordinate of each joint. The module STATEFLOW in MATLAB is used to simulate the entire stair-climbing process of WT wheelchair robot, and comparison is made between the output curves of each joint and the tension of the track and the expected reference input curves, which verifies the effectiveness of the proposed control law.     

Time‐varying linear controllers for exponential tracking of non‐holonomic systems in chained form

In this paper, the authors address the tracking problem for non‐holonomic systems in chained form with target signals that may exponentially decay to zero. By introducing a time‐varying co‐ordinate transformation and using the cascade‐design approach, smooth time‐varying controllers are constructed, which render the tracking‐error dynamics globally ??‐exponentially stable. The result shows that the popular condition of persistent excitation or not converging to zero for the reference signals is not necessary even for the globally ??‐exponential tracking of the chained‐form system. The effectiveness of the proposed controller is validated by simulation of two benchmark mechanical systems under non‐holonomic constraints. Copyright © 2006 John Wiley & Sons, Ltd.     

Linear matrix inequalities for analysis and control of linear vector second‐order systems

Many dynamical systems are modeled as vector second‐order differential equations. This paper presents analysis and synthesis conditions in terms of LMI with explicit dependence in the coefficient matrices of vector second‐order systems. These conditions benefit from the separation between the Lyapunov matrix and the system matrices by introducing matrix multipliers, which potentially reduce conservativeness in hard control problems. Multipliers facilitate the usage of parameter‐dependent Lyapunov functions as certificates of stability of uncertain and time‐varying vector second‐order systems. The conditions introduced in this work have the potential to increase the practice of analyzing and controlling systems directly in vector second‐order form. Copyright © 2014 John Wiley & Sons, Ltd.     

完整力学系统的三类对称性与三类守恒量

研究完整力学系统的Noether对称性、Lie对称性和形式不变性,以及由它们导致的Noether守恒量、Hojman守恒量和一类新型守恒量。     

周期时变线性系统的一般线性二次型最优控制

讨论周期时变线性系统的一般线性二次型最优控制问题, 即状态方程为非齐次方程且二次型性能指标包含线性项的一般情况. 给出了该问题可解的一系列充分必要条件, 同时给出了最优控制的解析构造以及最优性能指标值.     

A Lagrange duality characterisation for stability under arbitrary switching in switched positive linear systems

The present communication is concerned with uniform exponential stability, under arbitrary switching, in discrete-time switched positive linear systems. Lagrange duality is used in order to obtain a new characterisation for uniform exponential stability which is in terms of sets of inequalities involving each of the matrices that represent the modes of the system. These sets of inequalities are shown to generalise the classical linear Lyapunov inequality that characterises, in positive matrices, the property of being Schur. Each solution to these sets of inequalities is shown to provide a representation, in terms of a number of linear functionals, for a common Lyapunov function for the switched positive linear system. A result is further presented which conveys to, a conservative upper bound on the minimum required number of linear functionals (in the above mentioned representation), and also to a method for computing them. Our proof for the aforementioned characterisation is based on another (equivalent) characterisation, in terms of the solvability of a dynamic programming equation associated to the switched positive linear system, which is also reported in the paper. In particular, it is shown that the associated dynamic programming equation has at most one solution. And this solution is shown to be convex, monotonic, positively homogeneous, and it yields a common Lyapunov function for the switched positive linear system.     

Nonsingular prescribed‐time stabilization of a class of uncertain nonlinear systems: A novel coordinate mapping method

This article investigates the nonsingular prescribed‐time stabilization problem for p‐normal form systems. Two significant progresses are made for the first time as follows: First, a novel concept named coordinate mapping of time domain, is proposed to transform the nonsingular prescribed‐time convergence problem into the ordinary finite‐time convergence problem of transformed time‐varying system. Second, a set of new parameters are introduced to extend the existing adding a power integrator technique, such that the power restriction is removed. Based on above design procedure, a periodic controller is constructed to stabilize the state of the p‐normal form system into a small neighborhood of the equilibrium in prescribed time. Theoretical result is supported by numerical simulation.