跟踪微分系统解的研究

在已有的跟踪微分器理论的基础上,证明了跟踪微分器系统的解关于输入信号的连续性,并且为了便于考察跟踪微分器系统解的结构特点等性质,利用逼近函数设计了新型的跟踪微分器,进而证明了其解与具有不连续右端的跟踪微分器的解之间的等价关系.最后,给出了跟踪微分器应用于雷达跟踪目标运动状态的仿真计算结果,表明了由于其不依赖目标运动状态方程的特点,在实践应用中具有相当大的优势.     

二阶跟踪—微分器的频率特性

本文给出二阶跟踪—微分器的频率特性 ,此频率特性类似于二阶线性低通滤波器的频率特性 ,但具有线性系统所没有的优点 ,即通带内有较小的相移 ,且无谐振现象 .同时 ,文中指出频率特性与跟踪参数和正弦输入信号幅值之间的关系就是一个简单的“平移”     

ε-次微分与边际函数的解

借助ε-次微分讨论一类对偶边际函数的次微分,并得到此类函数解集的特征．     

新型离散跟踪-微分器的设计与分析

§ 1　 IntroductionAt present,difference method is often used forcomputing the differential coefficientofsignals.Since the error of this method is very obvious,it is not adapted to the systems ofhigh precision.There is a nonlinear tracking-differentiator(T-D) given in paper[1 ] ,whose precision is quite better than thatwith difference method.Itchanges the situation ofconsistent use of difference method.The designed tracking-differentiator has an analyticsolution,and has been applied to many …     

复微分-差分方程组的整函数解

利用值分布理论,研究了一类n阶复微分-差分方程ω~(n)(z)~2+[αω(z+c)-βω(z)]~2=1和复微分-差分方程组■是否存在有限级整函数解的问题.本文推广并改进了高凌云和刘凯等人的结果.     

两类复微分-差分方程组的整函数解

利用Nevanlinna值分布理论以及复差分和复微分理论,讨论了两类复微分-差分方程组的有限级超越整函数解问题,得到了两个结果,并将涉及微分或差分方程的某些结果推广至复微分-差分方程组中.     

非线性刚性微分-代数系统的波形松弛离散法

研究基于Runge-Kutta方法的波形松弛离散过程,得到新的刚性微分-代数系统的收敛理论,及该类系统解的存在性和惟一性,并用具体算例测试该理论的有效实用性.     

带有初态偏差的离散时滞系统控制策略

针对带有初态偏差的线性离散时滞系统,提出了一种带有修正初态偏差功能的迭代学习控制策略,该控制算法能够使得系统在某个指定区间达到逐点完全跟踪.该指定区间和时滞系统的时滞参数无关,并且该方法能够推广到多时滞系统中.在跟踪过程中,如果系统带有随机性扰动,应用本文所提算法,系统依然能够稳定.最后通过三个算例验证了算法的有效性.     

复微分方程组及复微分-差分方程解的级

利用Zalcman关于正规族的方法,研究了两类复高阶微分方程组的亚纯解的增长级问题;同时,利用Nevanlinna值分布理论,讨论了两类复微分-差分方程的超越整函数解的增长级.所得结论推广和改进了一些文献的结果,并举例说明本文的结论精确.     

改进的微分-差分特征列方法

基于高小山,J.Van der Hoeven等人2009年提出的微分-差分(DD)特征列方法理论,针对微分-差分系统的一些特性,在原有理论方法的基础上进行改进与补充,对升列,导元,约化等概念重新定义.提出了一则新算法(Seesaw),用来对多项式系统中的变量的类重新确定,目的是为在比较升列序的过程中重新对变量排序,在实际计算中可以降低系统求解的难度.另外对DD-伪余算法也进行了改进.     

有限时间迭代学习控制

针对任意初态情形, 借助于初始修正吸引子的概念,讨论不确定时变系统能够达到实际完全跟踪性能的迭代学习控制方法.闭环系统中含有限时间控制作用, 在预先指定的区间上实现零误差跟踪,且起始段的系统输出轨迹也可预先规划.分别讨论部分限幅学习与完全限幅学习, 证明闭环系统中各变量的一致有界性以及误差序列的一致收敛性. 变量有界性证明得益于提出的限幅学习算法,特别是完全限幅学习算法可确保参数估值的变化范围.     

带Morita对偶的偏序集环

设Ｒ是有１的结合环,Ｉ是任意偏序集,ＲＩ是Ｒ上Ｉ的偏序集环．本文考虑了带对偶的偏序集环,得到：ＲＩ带Ｍｏｒｉｔａ对偶当且仅当Ｒ带Ｍｏｒｉｔａ对偶．推广了已有的在Ｒ是有限偏序集时的有关结果     

Sur l'ideal d'ordre des operateurs AM-compacts

We give different necessary and sufficient conditions so that the space of AM-compact operators is an order ideal and we deduce some consequences. R´ESUME. Nous donnons différentes conditions nécessaires et suffisantes pour que l'espace des opérateurs AM-compacts soit un idéal d'ordre et nous déduisons quelques conséquences.

     

Optimal control of distributed parabolic systems with multiple time delays given in the integral form

Various optimal control problems for linear parabolic systemswith multiple time delays given in the integral form are considered.Necessary and sufficient conditions of optimality are derivedfor the Neumann problem. The optimal control is obtained inthe feedback form. Making use of the results of Schwartz, therepresentation of the optimal feedback control is given. A simpleexample of application is also provided.     

Existence of singular extremals and singular functionals in reachable spaces

Given a linear, infinite dimensional control system with point target and "full" control we show that singular extremals for the minimum norm problem exist except in certain exceptional cases ("singular" means "not satisfying Pontryagin's maximum principle"). Existence of singular extremals implies existence of certain functionals (also called singular) in the space of reachable states. Received March 5, 2001; accepted April 10, 2001.     

Impulsively-controlled systems and reverse dwell time: A linear programming approach

We present a receding horizon algorithm that converges to the exact solution in polynomial time for a class of optimal impulse control problems with uniformly distributed impulse instants and governed by so-called reverse dwell time conditions. The cost has two separate terms, one depending on time and the second monotonically decreasing on the state norm. The obtained results have both theoretical and practical relevance. From a theoretical perspective we prove certain geometrical properties of the discrete set of feasible solutions. From a practical standpoint, such properties reduce the computational burden and speed up the search for the optimum thus making the algorithm suitable for the on-line implementation in real-time problems. Our approach consists in approximating the optimal impulse control problem via a binary linear programming problem with a totally unimodular constraint matrix. Hence, solving the binary linear programming problem is equivalent to solving its linear relaxation. Then, given the feasible solution from the linear relaxation, we find the optimal solution via receding horizon and local search. Numerical illustrations of a queueing system are performed.     

Control of systems to sets and their interiors

For a closed target setS ⁿ and a control system (formulated as a differential inclusion and defined nearS), the present paper considers a sufficient condition for the property that every point nearS can be steered toS in finite time by some trajectory of the system. Estimates are obtained revealing how fast some such trajectory is nearing the target. A strong form of this condition is shown to imply that every trajectory of the system hits the target. With a further assumption on the target setS, we also consider conditions that guarantee that some trajectories enter the interior ofS.This work was supported by the Natural Sciences and Engineering Research Council of Canada and by FCAR, Québec, Canada.