随机最优控制的二阶必要条件综述

文章介绍作者(含合作)近期在随机最优控制的二阶必要条件方面的工作.首先,在凸控制约束情况下给出经典意义下随机奇异最优控制的逐点型二阶必要条件.其次,利用针状变分获得具有非凸控制约束的Pontryagin最大值原理意义下随机奇异最优控制的逐点型二阶必要条件.最后利用变分分析的工具进一步改进非凸控制约束情形的结果,并将其推广到具有状态约束的情形.     

机械多体系统动力学非线性最优控制问题的Noether理论

基于群不变性原理求解了机械多体动力学系统非线性最优控制问题的Noether型守恒定律.该文主要研究一类理想完整约束下的受控机械多刚体系统,通过增广向量法将动力学Euler-Lagrange方程以状态空间形式表示,利用变分法得到最优控制问题最优解的状态方程、伴随方程和控制方程,对系统性能指标泛函进行包含时间、状态变量、协态变量和控制变量的Noether对称无限小变换,进而得到最优解方程组的守恒量,使最优解关系以一组代数方程形式表达,为最优解的积分方法以及各种数值算法都奠定了坚实基础.最后,以基础振动下机械臂非线性动力学的能量最优控制实例分析,说明了该文对称性方法的正确性.     

一阶系统非线性边值问题的奇摄动*

本文应用比较定理研究了一类非线性边界条件的向量非线性奇摄动问题εx='f(t,x,y,e)εy'=g(t,x,y,ε)x(0)=A(ξ₁,ξ₂,x(1)-x(0),y(1)-y(0),ε)y(0)=B(ξ₁,ξ,x(1)-x(0),y(1)-y(0),ε)这里ξ₁,ξ₂为ε的函数。0<ε<<1,在适当的条件下,作出了任意次精度的渐近展式。并得出余项估计。     

一类改进的非线性种群系统的最优控制

研究某一类改进的关于年龄结构的非线性种群系统的最优控制问题.首先利用常用的极小化序列方法证明最优控制问题的最优解存在;其次定义原系统对应的共轭系统,借助于法锥定义,得到最优解所要满足的必要条件.     

具混合约束的最优控制的二阶必要条件

本文研究了一类具等式与不等式约束的最优控制问题．用Ledzewicz和Schattler引进的二阶锥概念,证明了一个含高阶微商项的局部最大值原理。     

一阶中立型差分方程振动的充分必要条件

本文研究了一阶常系数中立型时滞差分方程△[x(n)-px(n-(τ))]+qx(n-σ)=0的振动性.当p＞1时,通过构造若干适当的函数,我们分别得到了在Τ-σ＜1,(τ)-σ=1和(τ)-σ＞1三种情形下该方程振动的充分必要条件.     

一阶非线性时滞微分方程初值问题

本文利用上、下解方法讨论一阶非线性滞后型泛函微分方程初值问题解的存在性,给出了解存在的充分条件,并得到了解的迭代序列．     

一类四阶非线性系统的稳定性

本文利用“类比法”构造了一类四阶非线性系统的李雅普诺夫函数 ,导出了该系统的平凡解的稳定性条件     

一类四阶非线性系统的稳定性

本利用“类经法”构造了一类四阶非线性系统的李雅普诺夫函数,导出了该系统的平凡解的稳定性条件。     

一阶多智能体系统的一致性分析

研究一阶连续多智能体系统的一致性问题,其中每个智能体只能在一系列离散时刻上获得其相对邻居的状态信息,并且每个智能体的保持器的周期和采样器的周期是不同的.通过分析多智能体系统的稳定性,获得了一致性成立的充要条件,该条件揭示了交流拓扑、控制器增益、采样器的周期和保持器的周期的关系.最后,提供一个仿真例子以说明理论结果的有效性.     

SECOND-ORDER OPTIMALITY CONDITIONS FOR OPTIMAL CONTROL PROBLEMS GOVERNED BY 3-DIMENSIONAL NEVIER-STOKES EQUATIONS

This article is concerned with second-order necessary and sufficient optimality conditions for optimal control problems governed by 3-dimensional Navier-Stokes equations. The periodic state constraint is considered.     

NECESSARY AND SUFFICIENT CONDITIONS FOR OSCILLATION OF NONLINEAR NEUTRAL DIFFERENTIAL EQUATIONS

1 IntroductionRecently there wele a lot of activity concerning the oscillatory behavior ofsolutions of delay differential equations. We refer to the monographs [1,2,3,4].In particular, the oscillations and nonoscillations of solutions of the first orderneutral linear differential equation[x(t) -- p(t)x(t -- T)]' Q(t)x(t -- a) = 0 (*)have been investigated by many authors.In this paper, we consider the following first order nonlinear neutral diffe-rential equationwhereT) a E (0, co), al(t) …     

PERIODIC OPTIMAL CONTROL PROBLEMS GOVERNED BY SEMILINEAR PARABOLIC EQUATIONS WITH IMPULSE CONTROL

This paper is concerned with periodic optimal control problems governed by semilinear parabolic differential equations with impulse control.Pontryagin's maximum principle is derived.The proofs rely on a unique continuation estimate at one time for a linear parabolic equation.     

TIME OPTIMAL BOUNDARY CONTROL FOR SYSTEMS GOVERNED BY PARABOLIC EQUATIONS

In this paper we consider the systems governed, by parabolioc equations \[\frac{{\partial y}}{{\partial t}} = \sum\limits_{i,j = 1}^n {\frac{\partial }{{\partial {x_i}}}} ({a_{ij}}(x,t)\frac{{\partial y}}{{\partial {x_j}}}) - ay + f(x,t)\] subject to the boundary control \[\frac{{\partial y}}{{\partial {\nu _A}}}{|_\sum } = u(x,t)\] with the initial condition \[y(x,0) = {y_0}(x)\] We suppose that U is a compact set but may not be convex in \[{H^{ - \frac{1}{2}}}(\Gamma )\], Given \[{y_1}( \cdot ) \in {L^2}(\Omega )\] and d>0, the time optimal control problem requiers to find the control \[u( \cdot ,t) \in U\] for steering the initial state {y_0}( \cdot )\] the final state \[\left\| {{y_1}( \cdot ) - y( \cdot ,t)} \right\| \le d\] in a minimum, time. The following maximum principle is proved: Theorem. If \[{u^*}(x,t)\] is the optimal control and \[{t^*}\] the optimal time, then there is a solution to the equation \[\left\{ {\begin{array}{*{20}{c}} { - \frac{{\partial p}}{{\partial t}} = \sum\limits_{i,j = 1}^n {\frac{\partial }{{\partial {x_i}}}({a_{ji}}(x,t)\frac{{\partial p}}{{\partial {x_j}}}) - \alpha p,} }\{\frac{{\partial p}}{{\partial {\nu _{{A^'}}}}}{|_\sum } = 0} \end{array}} \right.\] with the final condition \[p(x,{t^*}) = {y^*}(x,{t^*}) - {y_1}(x)\], such that \[\int_\Gamma {p(x,t){u^*}} (x,t)d\Gamma = \mathop {\max }\limits_{u( \cdot ) \in U} \int_\Gamma {p(x,t)u(x)d\Gamma } \]     

EQUIVALENCE OF THREE DIFFERENT KINDS OF OPTIMAL CONTROL PROBLEMS FOR STOKES EQUATIONS

This article presents an equivalence theorem for three different kinds of optimal control problems,which are optimal target control problems,optimal norm control problems,and optimal time control problems.Controlled systems in this study are internally controlled Stokes equations.     

求解非线性互补问题的一种序列线性方程组方法

１　引　言 设Ｆ：Ｒｎ→Ｒｎ．则非线性互补问题ＮＣＰ（Ｆ）的形式如下：求ｘ∈ＲＮ,使ＮＣＰ（Ｆ）是如下变分不等式ＶＩ（Ｆ,Ｘ）的一种重要形式：求ｘ∈Ｘ　Ｒ　使当Ｘ＝Ｒｎ＋时,ＶＩ（Ｆ,Ｘ）即为ＮＣＰ（Ｆ）．由于ＮＣＰ和ＶＩ在工程和经济等领域中有广泛的应用,因而,对其研究受到了很大的重视．目前,关于（１．２）的求解已发展了一系列算法,线性化方法是常用的一类算法．线性化方法的局部收敛性研究已有了许多好的结果（见［９,１０］等）．全局收敛性成为了当前研究ＶＩ（Ｆ,Ｘ）算法的一个热门课题．并在Ｎｅｗｔｏ…     

VARIATIONAL DISCRETIZATION FOR OPTIMAL CONTROL GOVERNED BY CONVECTION DOMINATED DIFFUSION EQUATIONS

In this paper, we study variational discretization for the constrained optimal control problem governed by convection dominated diffusion equations, where the state equation is approximated by the edge stabilization Galerkin method. A priori error estimates are derived for the state, the adjoint state and the control. Moreover, residual type a posteriori error estimates in the L^2-norm are obtained. Finally, two numerical experiments are presented to illustrate the theoretical results.     

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：...     

求解非线性方程的最优8阶史蒂芬森方法

本文研究了非线性方程求根问题. 利用权函数方法, 获得了一种三步8阶收敛的史蒂芬森型方法. 实验结果表明本文提出的方法计算时间少于其它同阶的最优方法.