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林卫东 《纯粹数学与应用数学》1995,11(1):104-108
本文对具有状态终端约束、控制受限的非线性连续最优控制问题给出一种新的可实现的离散方法,此方法通过求解非线最小二乘问题避免这类问题离散后出现的不可行现象,文中给出这种做法的理论证明和实现方案。 相似文献
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当函数f(x,t,u)满足一些[1]中常假定的条件时,我们可借助算子S~(N)和不等式证明非线性奇异积分方程有唯一的离散近似解,这个解可用关于距离的逐次逼近法得到. 相似文献
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将积分区间划分为2N 等分后,我们定义了带位移的离散奇异算子■~(N).对于广义 Hilder 空间 H_(α,β,γ)中的函数 u(x),被带位移奇异算子作用后与■(N)_u 的差在分点处是 O((ln N)/(Nγ)).算子■(N)是一致有界的。利用它,我们给出了一类带位移的非线性奇异积分(哥西核)方程的离散近似解 相似文献
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一类带弱奇异核非线性偏积分微分方程的全离散有限元 总被引:1,自引:0,他引:1
1引言我们将研究下面一类带弱奇异核非线性偏积分微分方程的数值解:u_t-▽·(a(u)▽u)-integral from n=0 to tβ(t-s)△u(s)ds=f(u),x∈Ω,t∈(?),(1.1) u(·,t)=0,x∈(?)Ω,t∈J,(1.2) u(·,0)=v(x),x∈Ω,(1.3)其中Ω为平面上的凸角域,J=(0,T],α和f为R上的光滑函数,满足0相似文献
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1 引言文章考虑如下形式的非线性奇异摄动差分方程:ε·{(g(y_(k+1))-2g(y_k)+g(y_(k-1)))/h~2}+(f(y_(k+1))-f y_k))(/h+H(x_k,y_k)=0, (1.1) y_0=α,y_N=β 相似文献
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主要研究基于有界控制律的一类非线性离散系统的奇异H∞控制问题.在系统不满足正则条件的情况下,分离出正则部分与非正则部分,给出基于有界反馈与二次Lyapunov函数的离散系统奇异H∞问题可解性的必要条件以及充分条件,求出的有界控制律能使得闭环系统在保证内稳定的条件下达到干扰衰减. 相似文献
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该文讨论了一类状态变量约束下由发展方程导出的最优控制系统,通过原问题的扰动,得到了状态变量与控制变量分离的最优性条件. 相似文献
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Let a trajectory and control pair
maximize globally the functional g(x(T)) in the basic optimal control problem. Then (evidently) any pair (x,u) from the level set of the functional g corresponding to the value g(
(T)) is also globally optimal and satisfies the Pontryagin maximum principle. It is shown that this necessary condition for global optimality of
turns out to be a sufficient one under the additional assumption of nondegeneracy of the maximum principle for every pair (x,u) from the above-mentioned level set. In particular, if the pair
satisfies the Pontryagin maximum principle which is nondegenerate in the sense that for the Hamiltonian H, we have along the pair
on [0,T], and if there is no another pair (x,u) such that g(x(T))=g(
(T)), then
is a global maximizer. 相似文献
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The accurate solution of optimal control problems is crucial in many areas of engineering and applied science. For systems which are described by a nonlinear set of differential-algebraic equations, these problems have been shown to often contain multiple local minima. Methods exist which attempt to determine the global solution of these formulations. These algorithms are stochastic in nature and can still get trapped in local minima. There is currently no deterministic method which can solve, to global optimality, the nonlinear optimal control problem. In this paper a deterministic global optimization approach based on a branch and bound framework is introduced to address the nonlinear optimal control problem to global optimality. Only mild conditions on the differentiability of the dynamic system are required. The implementa-tion of the approach is discussed and computational studies are presented for four control problems which exhibit multiple local minima. 相似文献
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In this article, we investigate the superconvergence of the finite element approximation for optimal control problem governed by nonlinear elliptic equations. The state and co-state are discretized by piecewise linear functions and control is approximated by piecewise constant functions. We give the superconvergence analysis for both the control variable and the state variables. Finally, the numerical experiments show the theoretical results. 相似文献
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In this work, the authors considered the periodic optimal control problem of Fitzhugh-Nagumo equation. They firstly prove the existence of time-periodic solution to Fitzhugh-Nagumo equation. Then they show the existence of optimal solution to the optimal control problem, and finally the first order necessary condition is obtained by constructing an appropriate penalty function. 相似文献
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This paper deals with the optimal control problems with multiple integrals and an elliptic partial differential equation. The sufficient conditions for optimality in these problems are proved through a dual dynamic programming. The concept of an optimal dual feedback is introduced, and the theorem guaranteeing its existence is established. For the purposes of numerical methods, the ε-version of the verification theorem provided appears to be very useful. 相似文献
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I. Bykadorov A. Ellero S. Funari E. Moretti 《Journal of Optimization Theory and Applications》2009,142(1):55-66
We consider optimal control problems with functional given by the ratio of two integrals (fractional optimal control problems). In particular, we focus on a special case with affine integrands and linear dynamics with respect to state and control.
Since the standard optimal control theory cannot be used directly to solve a problem of this kind, we apply Dinkelbach’s approach
to linearize it. Indeed, the fractional optimal control problem can be transformed into an equivalent monoparametric family
{Pq} of linear optimal control problems. The special structure of the class of problems considered allows solving the fractional
problem either explicitly or requiring straightforward classical numerical techniques to solve a single equation. An application
to advertising efficiency maximization is presented.
This work was partially supported by the Università Ca’ Foscari, Venezia, Italy, the MIUR (PRIN cofinancing 2005), the Council
for Grants (under RF President) and State Aid to Fundamental Science Schools (Grant NSh-4113.2008.6).
We thank Angelo Miele, Panos Pardalos and the anonymous referees for comments and suggestions. 相似文献
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We show that the value function of a singular stochastic
control problem is equal to the integral of the value function
of an associated optimal stopping problem. The connection is
proved for a general class of diffusions using the
method of viscosity solutions. 相似文献
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We show that the value function of a singular stochastic
control problem is equal to the integral of the value function
of an associated optimal stopping problem. The connection is
proved for a general class of diffusions using the
method of viscosity solutions. 相似文献
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强非线性问题的改进的L-P解法 总被引:12,自引:0,他引:12
用改进的L-P法求解了一类平方强非线性自由振动问题和一类非振动型的强非线性问题,得到了精度很好的一级近似解,方法与通用的改进的L-P法稍有不同。 相似文献