本质线性非完整系统的Hamilton原理

研究了本质线性非完整系统的Hamilton原理,分别应用与不应用Appell-Chetaev条件证明了本质线性非完整系统Hamilton变分泛函取驻值的充分必要条件.结果表明,在本质线性非完整系统中,Hamilton作用量是稳定的作用量,与完整系统的Hamilton原理具有相同的形式与本质;而且由Hamilton原理得到的运动方程不会导致任何力学与数学上的矛盾.最后给出了Hamilton原理向本质非线性非完整系统推广时产生数学与力学上不合理的根本原因.     

本质线性非完整系统的Hamilton的原理

研究了本质线性非完整系统的Hamilton原理，分别应用与不应用Appell—Chetaev条件证明了本质线性非完整系统Hamilton变分泛函取驻值的充分必要条件．结果表明，在本质线性非完整系统中，Hamilton作用量是稳定的作用量，与完整系统的Hamilton原理具有相同的形式与本质；而且由Hamilton原理得到的运动方程不会导致任何力学与数学上的矛盾．最后给出了Hamilton原理向本质非线性非完整系统推广时产生数学与力学上不合理的根本原因。     

经典非完整Appell Hamel约束的性质

研究了非完整约束Appell-Hamel例.证明了经典Appell-Hamel例对于非完整系统的Hamilton作用量是稳定值.研究了该约束对于非完整力学Rosen-Edelstein模型的解,证明了对于三个非完整力学模型Ap-pell-Hamel例具有相同解.利用非完整力学系统可归结为有条件的完整系统的理论,得出了经典Appell-Hamel例具有第二类Lagrange方程的形式.     

一种线性约束规划问题的神经网络模型及其应用

提出了一种基于梯度投影矩阵下的求解线性约束下规划问题的神经网络。针对解的稳定性问题,导出了该网络相关参数之间的关系。由文中定义可知,该网络不但适合于求解线性约束下线性或非二次规划问题,而且也用于求解线性或非线性方程组问题,比其它规划问题的神经网络方法更具有一般性。     

非线性系统的实现与最小阶问题

在系统的微分域及相应的微分向量空间上定义了一个非交换的多项式环(算子环), 并利用这个环定义非线性系统的传递函数.用微分向量空间为工具,讨论单输入/单输出非线 性系统的实现问题.主要结果回答了:1)在什么条件下,不同的输入/输出微分方程有相同(等 价)的实现;2)在未知实现的条件下,如何确定输入/输出微分方程最小实现的阶数.覆盖了线 性系统理论的相关结果.     

力学与控制科学

基于对力学与控制科学的相似性的分析,阐述了4个有意义的力学系统控制问题:① 具非完整约束的非线性动力学系统的控制;②具非单一平衡位置的力学系统及其总体性质;③ 多体动力学与控制;④具分布参数的力学系统.最后给出了一个具启示性的看法.     

事件空间中非完整力学系统的Herglotz-d′Alembert原理与守恒律

研究事件空间中非完整力学系统的Herglotz型守恒律.给出事件空间中Herglotz型广义变分原理,引入非完整约束并采用交换关系的H9lder定义,导出事件空间中非完整力学系统的新型微分变分原理—Herglotz-d′Alembert原理.引进事件空间中的空间生成元和参数生成元,建立Herglotz-d′Alembert原理不变性条件的变换.基于该原理构建了事件空间中非完整非保守力学系统的Herglotz型守恒定理及其逆定理.作为特例,给出了位形空间的Herglotz型守恒量和事件空间中完整力学系统的Herglotz型守恒量.文末还给出了一个算例.     

无约束非线性规划的数值方法

在自动控制、科学管理和其它一些科学领域中，很多问题可以归结为线性规划。但是，还有另外一些问题，其目标函数和约束条件却很难用线性函数来表达。我们称这种数学规划为非线性规划。1951年，库恩（Kuhn）一塔克（Tucker）提出了处理非线性规划问题的完整理论，得到一组不等式约束最优化问题的必要条件，称为库恩一塔克定理，非线性规划到目前为止，还没有适用于各种问题的一般算法。各个方法都有自己特定的适用范围。优化包括数学规划的全部内容，最简单的优化问题是无约束最优化，对这类问题，已经研究出比较有效的求解方法，因而构成…     

一类非线性随机不确定系统有限时间H∞无穷滤波

研究一类具有时变、有界干扰的非线性随机不确定系统有限时间H∞滤波问题.首先,给出了非线性随机不确定系统有限时间H∞滤波问题的定义;其次,通过构造Lyapunov-Krasoviskii函数,并结合线性矩阵不等式（LMI）方法,给出了非线性随机不确定系统有限时间∞滤波器存在的充分条件;再次,将该问题简化为具有LMI约束的优化问题,并给出了相应的求解算法;最后,通过数值算例表明了所提出设计方法的有效性.     

非线性预测控制研究的进展及其若干问题的思考

非线性预测控制是将已日趋成熟的线性预测控制向非线性领域方面的延伸与扩展.介绍了非线性预测控制的产生背景、主要原理、发展的迫切性以及发展前景,针对非线性系统所具有的特点,分析了其在发展中存在的问题,以及今后发展中需要解决的问题,同时就约束问题、稳定性、鲁棒性、输出反馈方面的研究进行了介绍和分析.论述了非线性预测控制与智能控制相结合的必然性.     

Modeling for dynamics of rigid-body systems with friction by linear complementary problem (LCP)

The purpose of this paper is to study the modeling method for nonholonomic systems with friction by linear complementary problem (LCP). Firstly, the dynamic equation with multipliers for the nonholonomic system with friction is given. Secondly, a standard linear complementary model is established, which describes the normal and tangential characteristics for a nonholonomic system. Thirdly, by using LCP theory, a general criterion is obtained, which can identify the singularity induced by nonideal geometrical constraints in a nonholonomic system. By a typical example of a nonholonomic system with friction, it is revealed how the problem solving for the constraint reaction forces can be transformed into the standard linear complementary problem. The research work may provide reliable theoretical basis for the dynamical simulation of a nonholonomic system with non-smooth factors.     

一种球形机器人的非线性滑模运动控制

基于非线性滑模控制方法,对一种欠驱动的球形机器人的运动控制问题进行了研究．球形机器人的输入由两个相互正交的力矩组成．在非完整约束的条件下,分别建立球形机器人的运动学和动力学模型,并通过输入变换将动力学模型变换为一个两输入的二阶系统．基于非线性滑模控制方法分别设计了横向姿态控制器和纵向速度控制器,可以保证被控的运动状态收敛到期望的邻域内．仿真和实验结果验证了所建立的动力学模型和控制方法的有效性．     

求解含非线性参数的QoS路由的启发式算法

具有非线性参数的QoS路由分为含有非线性约束条件的QoS路由和含有非线性优化目标的QoS路由两类，它们都是NP问题．提出了两种启发式算法求解这两类QOS路由优化问题问题．对第一类问题，求解去掉非线性约束条件后的优化问题．如果找到的解满足非线性约束条件，则该解是最优解；否则在优化问题中添加一个新的线性约束，将已得到的解去掉，反复下去就可得到最终解．对第二类问题，将非线性优化目标换为约束条件中的线性参数，求解此优化模型，如果有解，则记录此时对应的非线性目标值．而后增加一个新的线性约束，去掉刚才得到的解，比较两次得到的非线性目标值，保留最小值．如果得到的解不满足该线性参数的约束条件，则算法结束；否则继续迭代．证明了两种算法的收敛性，并且时间复杂性为近似多项式时间．计算实例表明了算法的有效性．     

Solvability of reactions in rigid multibody systems with redundant nonholonomic constraints

The problem of calculating joint reaction forces in rigid body mechanisms with redundant constraints, both geometric and nonholonomic, is discussed. When constraint equations are dependent, some of the constraint reactions are unsolvable, i.e., cannot be uniquely determined using a rigid body model, whereas some others may be solvable. In this paper, analytic conditions, which must be fulfilled to obtain unique values of selected reaction forces in the presence of dependent nonholonomic constraints, are presented and proven. The concept of direct sum, known from linear algebra, is exploited. These purely mathematical conditions are followed by numerical methods that enable detection of constraints with uniquely solvable reactions. Similar conditions and methods were proposed earlier for holonomic systems. In this contribution, they are generalized to the case of linear nonholonomic constraints. An example of constraint reactions solvability analysis, for a mechanism subjected to redundant nonholonomic constraints, is presented.     

A Methodological View of Constraint Solving

Constraints are an effective tool to define sets of data by means of logical formulae. Our goal here is to survey the notion of constraint system and to give examples of constraint systems operating on various domains, such as natural, rational or real numbers, finite domains, and term domains. We classify the different methods used for solving constraints, syntactic methods based on transformations, semantic methods based on adequate representations of constraints, hybrid methods combining transformations and enumerations. The concepts and methods are illustrated via examples. We also discuss applications of constraints to various fields, such as programming, operations research, and theorem proving.     

一种有指导的轮式机器人全局规划方法*

非完整系统的运动规划是尚未得到充分的重要问题，本文把全局规划方法与局部规划方法结合起来，提出一种包含非完整约束条件的有指导的全局运动规划方法，，并通过仿真验证了其可行性。     

Hybrid Fuzzy Model-Based Control of Nonholonomic Systems: A Unified Viewpoint

This paper proposes a unified hybrid fuzzy model-based control scheme for uncertain nonholonomic systems. Compared with typical hybrid fuzzy control, the stability analysis is performed based on a new concept of constructing a semicommon Lyapunov function and a new definition called as exponential-like model following. This advancement provides a strict stability analysis but results in relaxed gain conditions. In detail, a unified hybrid Takagi-Sugeno fuzzy model is first introduced for representing well-known nonholonomic systems with a momentum conservation constraint or a no-slip constraint. Then, the hybrid fuzzy controller is derived to ensure robust nonlinear model following control, i.e., an asymptotic convergence with adjustable ultimate bound and arbitrary disturbance attenuation in an -gain sense. Furthermore, an iterative linear matrix inequality technique is proposed to guarantee the stability and avoid the need of a common positive-definite matrix. Finally, the applications are carried out on a hopping robot and a car-like mobile robot. Numerical simulations and experiment results show the expected performances.     

Teaching Macroeconomics with GAMS

Our general goal in this paper is to show how to implement in GAMS standard deterministic nonlinear macro models, and stochastic linear macro models with rational expectations. We will also present basic concepts on solution methods and policy analysis for these kinds of models. As a practical illustration, we will use some well known teaching and experimental models in the macroeconomic literature.     

A definition of column reduced proper rational matrices

The aim of this work is to develop analogue concepts of column reduced polynomial matrices for proper rational matrices. A definition of column reducedness for a class of proper rational matrices is proposed and the properties of such matrices are studied, in particular reduction to column reduced form by elementary operations over the ring of proper rational functions, and the relationship between the degrees of the invariant factors of a column reduced matrix and the so-defined column indices. The physical significance of such matrices in terms of their finite structure is explained; this interpretation completely complements the physical interpretation of a column reduced polynomial matrix. An application of the properties of column reduced proper rational matrices to the decoupling problem is also presented: the infinite structure which can be obtained while decoupling a linear multivariable system by non-regular static state feedback is completely characterized.