OPTIMAL CONTROL OF A CLASS OF DISTRIBUTED PARAMETER DELAY SYSTEMS

In this paper we consider the optimal control problem for a class of infinite dimensional delay evolution systems whose principal operator is the infinitesimal generator of an analytic semigroup. We give an existence result of α - solutions of the controlled systems and prove the existence of solutions for an extremal problem subject to such systems. In particular, the necessary conditions of optimality for the same problem are presented.     

k-STABILITY OF NONLINEAR NEUTRAL DELAY SYSTEMS

In this paper,we first introduce the concept of k-globally asymptotic stabi- lity and present a differential-difference inequality with infinite delay.By com- bining nonlinear inequality and nonlinear variation-of-parameters formula,we derive the k-globally asymptotic stability criteria for nonlinear neutral system with infinite delay.In the end of this paper,an example is given to illustrate our theory.     

关于人口系统妇女总和生育率的范数最优控制问题

本文讨论人口系统妇女总和生育率的范数最优控制问题。本文将妇女总和生充臃当作控制变量，在一定条件下证得最优控制的存在和唯一性，并给出其相应的优化条件。     

EXISTENCE OF FORECAST AND DECISION HORIZONS FOR OPTIMAL CONTROL PROBLEMS OF NONLINEAR SYSTEMS

ＥＸＩＳＴＥＮＣＥＯＦＦＯＲＥＣＡＳＴＡＮＤＤＥＣＩＳＩＯＮＨＯＲＩＺＯＮＳＦＯＲＯＰＴＩＭＡＬＣＯＮＴＲＯＬＰＲＯＢＬＥＭＳＯＦＮＯＮＬＩＮＥＡＲＳＹＳＴＥＭＳ￥ＺｈａｎｇＣｈｅｎｇｙｕｎ（张成云）（ＦｕｄａｎＵｎｉｖｅｒｓｉｔｙ，复旦大学，邮编：...     

在不确定观测下离散状态时滞系统的最优滤波

研究了在不确定观测下离散状态时滞系统的最优滤波问题,观测值的不确定性则通过一个满足Bernoulli分布且统计特性已知的随机变量来描述. 一般采用状态增广方法将时滞系统转换为无时滞随机系统, 再利用Kalman滤波器的设计方法解决最优状态估计问题, 但是当系统时滞较大时,转换后的系统状态维数很高, 这样增加了计算负担. 为此,基于最小方差估计准则, 利用射影性质和递归射影公式得到了一个新的滤波器设计方法, 而且保证了滤波器的维数与原系统相同.最后, 给出一个仿真例子说明所提方法的有效性.     

PERIODIC SOLUTIONS OF DELAY DIFFERENTIAL EQUATIONS WITH TWO DELAY VIA BI-HAMILTONIAN SYSTEMS

1 Illtroduction and Statement of the Main ResultIn this paper, we shall study the existence of periodic solutions for the twofOllowing differential delay equationsX'(t) = --f(x(t -- r1))g(x(t -- r2)) -- f(x(t -- r2))g(x(t -- r1)), (1)andX'(t) = f(x(t -- rl))g(x(t -- r2)) f(x(t -- r2))g(x(t -- rl)), (2)where ri (i = l,2) are positive constants. When the function g(x) = 1,equations (1) and (2) become respectivelyIn 1974, Kaplan and Yorke (see [101) proved the existence of periodic so1utions…     

中立型线性控制系统的最优控制

本文将就形如　的中立型线性控制系统进行深入讨论，给出此类系统的最优控制的最大值原理，并举例说明这一重要结论在经济管理系统中的应用。     

退化时滞微分系统的全时滞稳定性

本文利用复Lyapunov方程给出了退化时滞微分系统全时滞渐近稳定的充要条件。     

退化时滞微分方程的周期解问题

本文讨论退化时滞微分方程的周期解问题．特别地，我们给出二维退化滞后微分方程的周期解的存在性问题，并在最后举例说明其应用。     

有限时滞随机微分输出系统的p阶矩有界性(英文)

本文研究了有限时滞随机微分输出系统的p阶矩有界性. 利用Liapunov第二方法和Razumikhin型条件,获得了关p阶矩一致有界、p阶矩一致有界且最终有界、p阶矩一致有界且一致最终有界的一些充分条件.     

THE STABILITY OF LINEAR MULTISTEP METHODS FOR SYSTEMS OF DELAY DIFFERENTIAL EQUATIONS

This paper deals with the numerical solution of initial value problems for systems of differential equations with a delay argument. The numerical stability of a linear multistep method is investigated by analysing the solution of the lest equation y'(t)=Ay(t) + By(1-t),where A,B denote constant complex N×N-matrices,and t>0.We investigate carefully the characterization of the stability region.     

STABILITY OF TIME VARYING SINGULAR DIFFERENTIAL SYSTEMS WITH DELAY

In this paper, stability of time varying singular differential systems with delay is considered. Based on variation formula and Gronwall-Bellman integral inequality, we obtain the exponential estimation of the solution and the sufficient conditions under which the considered system is stable and exponentially asymptotically stable. These results will be very useful to further research on Roust stability and control design of uncertain singular control systems with delay.     

POSITIVE PERIODIC SOLUTIONS OF PREDATOR-PREY SYSTEMS WITH INFINITE DELAY

1.IntroductionPredator-preysystemsareonekindsofecologicalsystems,theyhaveattractedmuchattentioninrecentyears.Butuptonow,mostoftheknownresultsareconcernedwithsystemswithouttimedelayorwithfinitedelay[1-6].Infinitedelaywillcausemuchmoretroublethanfinitedelaydoes,andcorrespondingresultsaremuchfewe.[7-9].Inthispaper,usingthepersistenceconclusionsof[9],weintroduceanewargument;withoututilizingcomplicatedphasespacetheory,changingtheperiodicsolutionproblemofinfinitedelaytotheoneoffinitedelay,newandbrie…     

DELAY DEPENDENT ROBUST DISSIPATIVE CONTROL FOR A CLASS OF NONLINEAR TIME-DELAY SYSTEMS

We discuss the delay dependent robust dissipative problem for a class of time-delay systems with nonlinear perturbations. And the sufficient conditions for the delay dependent robust dissipation and quadratic stability are given by the linear matrix inequalities (LMIs), then the time-delay bound and the delay dependent robust dissipative state feedback controller are presented.     

VARIATIONAL DISCRETIZATION OF A CONTROL-CONSTRAINED PARABOLIC BANG-BANG OPTIMAL CONTROL PROBLEM

We consider a control-constrained parabolic optimal control problem without Tikhonov term in the tracking functional.For the numerical treatment,we use variational discretization of its Tikhonov regularization:For the state and the adjoint equation,we apply Petrov-Galerkin schemes in time and usual conforming finite elements in space.We prove a-priori estimates for the error between the discretized regularized problem and the limit problem.Since these estimates are not robust if the regularization parameter tends to zero,we establish robust estimates,which--depending on the problem's regularity——enhance the previous ones.In the special case of bang-bang solutions,these estimates are further improved.A numerical example confirms our analytical findings.     

STABILITY OF DELAY DIFFERENTIAL SYSTEMS BY SEVERAL LIAPUNOV FUNCTIONS

1 IntroductionConsider the functional differential equations (FDE's) with finite delay ofthe form:where x,(0) = x(t 0) for --r 5 0 5 0 with some r 2 0 and f: [T, co] x C RI with C = C([--r, 0], R') the space of continuous functions mapping [--r, 0]into l-dimensional real space RI. For any yi E C we define the norm of yi as:where l' I is any norm in RI.Inspired by the ideas in [l--3], we develop a new technique in this work tostudy the stability of FDE's, where the components xl) xZt…     

一类随机时延网络控制系统的神经网络自适应容错控制

针对一类随机时延网络控制系统,提出一种基于RBF神经网络自适应动态补偿的容错控制策略.该方法通过在线估计时延将系统建模为随机切换系统,并在模型参考自适应方法的基础上设计RBF神经网络动态补偿容错控制器,利用Lyapunov稳定性理论给出神经网络补偿器的在线权值学习算法,以保证网络控制系统在故障情况下的跟踪性能和状态一致最终有界稳定.最后通过仿真验证了该方法的有效性.     

具有扩散和常捕获量及反馈控制的Logistie滞后系统的振动性

本文对含有扩散和常捕获量及反馈控制的Ｌｏｇｉｓｔｉｃ滞后模型进行了讨论，分别获得了一些关于正平衡态振动的充分条件．     

AN EFFICIENT METHOD FOR MULTIOBJECTIVE OPTIMAL CONTROL AND OPTIMAL CONTROL SUBJECT TO INTEGRAL CONSTRAINTS

We introduce a new and efficient numerical method for multicriterion optimal control and single criterion optimal control under integral constraints. The approach is based on extending the state space to include information on a ＂budget＂ remaining to satisfy each constraint; the augmented Hamilton-Jacobi-Bellman PDE is then solved numerically. The efficiency of our approach hinges on the causality in that PDE, i.e., the monotonicity of characteristic curves in one of the newly added dimensions. A semi-Lagrangian ＂marching＂ method is used to approximate the discontinuous viscosity solution efficiently. We compare this to a recently introduced ＂weighted sum＂ based algorithm for the same problem [25]. We illustrate our method using examples from flight path planning and robotic navigation in the presence of friendly and adversarial observers.