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设u(x,t)=(SΩf)(x,t)是一般色散初值问题(?)tu-iΩ(D)u=0,u(x,0)=f(x),(x,t)∈Rn×R的解,SΩ*f,SΩ**f是它的局部和整体极大算子.本文给出它们范数的若干估计. 相似文献
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本文获得了如下的奇异半线性反应扩散方程初值问题{(e)u/(e)t-(1/tσ)△u=up+f(x),t>0,x∈Rnlim t→0+ u (t,x)=0, x∈Rn广义解(mild solution)在L∞ loe[(0,∞);L∞(Rn)]中的存在性.其中σ>0,0<p<1,f(x)非负且f(x)∈L∞(Rn). 相似文献
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非自治系统的周期解 总被引:5,自引:1,他引:4
§1.(?)=f(t,x)的周期解考虑一般情形(?)=f(t,x),x∈R~n,(1.1)其中 f(t,x)是连续的以ω为周期的周期函数.引入下列记号:B_ω={u(t);u(t)∈C_([0,ω]),u(0)=u(ω)}‖u‖=(?)|u(t)|,对 u(t)∈B_ω.则 B_ω为一 Banach 空间.再记B_1={u(t);u(t)∈B_ω,且对任意 t∈[0,ω] u(t)=u(0)},B_2={u(t);u(t)∈B_ω,且 integral from n=0 to ω u(t)dt=0},则 B_1∩B_2={0}.B_ω有直和分解 B_ω=B_1(?)B_2,且 相似文献
5.
无约束连续最优控制问题的离散序列二次规划方法 总被引:1,自引:1,他引:0
其中f_0:R~n×R~m×R→R,g_0:R~n→R,f:R~n×R~m×R→R~n关于它们各自变量二次连续可微。终端时间T固定,初始状态已知,x(t)为状态变量,u(t)为控制变量,问题要求选择适当的 u(t)使目标函数(1.1)达到极小。 求解此类问题的一种途径是通过离散时间函数x(t),u(t)将它转化成传统的数学规划问题,然后,利用数学规划中已有的方法求得原问题的近似解。Cullum,Budak等在[1]和 相似文献
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In this paper we consider the Cauchy Problem for the mass-critical Hartree equation I(e)tu △u=μ(|x|2*|u|2)u,(t,x)∈R×Rn,n≥3,(1) u(0,x)=φ(x), x∈Rn,(2) 相似文献
7.
林文贤 《应用数学与计算数学学报》1989,3(1):92-94
本文讨论下述定解问题的差分解法 u_t(x,t)=Au_(xx)(x,t) f(u),(x,t)∈Q_T=(0,L)×(0,T) u_x(0,t)—σ_1u(0,t)=0,σ_1>0,t∈[0,T]; u_x(L,t) σ_2u(L,t)=0,σ_2>0,t∈[0,T]; u(x,0)=■(x),x∈[0,L].其中u(x,t)=(u_1(x,t),…,u_m(x,t)),f(u)=f(f_1(u),…,f_m(u)),■(x)=(■_1(x),…■_m(x))满足适定性条件,且假定 相似文献
8.
1 引 言考虑下述非线性双曲型方程的混合问题:c(x,u)utt-.(a(x,u)u)=f(x,u,t), x∈Ω,t∈J,(1.1)u(x,0)=u0(x), x∈Ω,(1.2)ut(x,0)=u1(x), x∈Ω,(1.3)u(x,t)=-g(x,t), (x,t)∈Ω×J,(1.4)其中ΩR2是一具有Lipschitz边界Ω的有界区域,J=[0,T],0相似文献
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《高等学校计算数学学报》2015,(1)
<正>1引言考虑非线性时滞控制系统初值问题y'(t)=f(y(t),y(t-T),u(t)),t≥0‘,y(t)=φ(t),-t≤t≤o,(1)这里T0为实常数,f:CdxCdxCq→Cd连续可微且满足f(0,0,0)=0,y(t)∈Cd表示状态函数,u(t)∈Cq表示控制函数,且当t≤0时,u(t)=0表示没有控制, 相似文献
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§1 IntroductionIn this paper we analyze an interior point scaling projected reduced Hessian methodwith trust region strategy for solving the nonlinear equality constrained optimizationproblem with nonnegative constraints on variables:min f(x)s.t. c(x) =0 (1.1)x≥0where f∶Rn→R is the smooth nonlinear function,notnecessarily convex and c(x)∶Rn→Rm(m≤n) is the vector nonlinear function.There are quite a few articles proposing localsequential quadratic programming reduced Hessian methods… 相似文献
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Joris T. Olympio 《Journal of Optimization Theory and Applications》2013,158(3):687-716
The paper describes a continuous second-variation method to solve optimal control problems with terminal constraints where the control is defined on a closed set. The integration of matrix differential equations based on a second-order expansion of a Lagrangian provides linear updates of the control and a locally optimal feedback controller. The process involves a backward and a forward integration stage, which require storing trajectories. A method has been devised to store continuous solutions of ordinary differential equations and compute accurately the continuous expansion of the Lagrangian around a nominal trajectory. Thanks to the continuous approach, the method adapts implicitly the numerical time mesh and provides precise gradient iterates to find an optimal control. The method represents an evolution to the continuous case of discrete second-order techniques of optimal control. The novel method is demonstrated on bang–bang optimal control problems, showing its suitability to identify automatically optimal switching points in the control without insight into the switching structure or a choice of the time mesh. A complex space trajectory problem is tackled to demonstrate the numerical robustness of the method to problems with different time scales. 相似文献
12.
Bin Li Chang Jun Yu Kok Lay Teo Guang Ren Duan 《Journal of Optimization Theory and Applications》2011,151(2):260-291
In this paper, we consider a class of optimal control problems subject to equality terminal state constraints and continuous
state and control inequality constraints. By using the control parametrization technique and a time scaling transformation,
the constrained optimal control problem is approximated by a sequence of optimal parameter selection problems with equality
terminal state constraints and continuous state inequality constraints. Each of these constrained optimal parameter selection
problems can be regarded as an optimization problem subject to equality constraints and continuous inequality constraints.
On this basis, an exact penalty function method is used to devise a computational method to solve these optimization problems
with equality constraints and continuous inequality constraints. The main idea is to augment the exact penalty function constructed
from the equality constraints and continuous inequality constraints to the objective function, forming a new one. This gives
rise to a sequence of unconstrained optimization problems. It is shown that, for sufficiently large penalty parameter value,
any local minimizer of the unconstrained optimization problem is a local minimizer of the optimization problem with equality
constraints and continuous inequality constraints. The convergent properties of the optimal parameter selection problems with
equality constraints and continuous inequality constraints to the original optimal control problem are also discussed. For
illustration, three examples are solved showing the effectiveness and applicability of the approach proposed. 相似文献
13.
Many practical optimal control problems include discrete decisions. These may be either time-independent parameters or time-dependent
control functions as gears or valves that can only take discrete values at any given time. While great progress has been achieved
in the solution of optimization problems involving integer variables, in particular mixed-integer linear programs, as well
as in continuous optimal control problems, the combination of the two is yet an open field of research. We consider the question
of lower bounds that can be obtained by a relaxation of the integer requirements. For general nonlinear mixed-integer programs
such lower bounds typically suffer from a huge integer gap. We convexify (with respect to binary controls) and relax the original
problem and prove that the optimal solution of this continuous control problem yields the best lower bound for the nonlinear
integer problem. Building on this theoretical result we present a novel algorithm to solve mixed-integer optimal control problems,
with a focus on discrete-valued control functions. Our algorithm is based on the direct multiple shooting method, an adaptive
refinement of the underlying control discretization grid and tailored heuristic integer methods. Its applicability is shown
by a challenging application, the energy optimal control of a subway train with discrete gears and velocity limits.
相似文献
14.
K. Malanowski 《Journal of Optimization Theory and Applications》1987,53(3):429-449
A family of optimal control problems for discrete systems that depend on a real parameter is considered. The problems are strongly convex and subject to state and control constraints. Some regularity conditions are imposed on the constraints.The control problems are reformulated as mathematical programming problems. It is shown that both the primal and dual optimal variables for these problems are right-differentiable functions of a parameter. The right-derivatives are characterized as solutions to auxiliary quadratic control problems. Conditions of continuous differentiability are discussed, and some estimates of the rate of convergence of the difference quotients to the respective derivatives are given. 相似文献
15.
A Haar wavelet technique is discussed as a method for discretizing the nonlinear system equations for optimal control problems.
The technique is used to transform the state and control variables into nonlinear programming (NLP) parameters at collocation
points. A nonlinear programming solver can then be used to solve optimal control problems that are rather general in form.
Here, general Bolza optimal control problems with state and control constraints are considered. Examples of two kinds of optimal
control problems, continuous and discrete, are solved. The results are compared to those obtained by using other collocation
methods. 相似文献
16.
K. Malanowski 《Applied Mathematics and Optimization》1984,12(1):231-245
A family of convex optimal control problems that depend on a real parameterh is considered. The optimal control problems are subject to state space constraints.It is shown that under some regularity conditions on data the solutions of these problems as well as the associated Lagrange multipliers are directionally-differentiable functions of the parameter.The respective right-derivatives are given as the solution and respective Lagrange multipliers for an auxiliary quadratic optimal control problem subject to linear state space constraints.If a condition of strict complementarity type holds, then directional derivatives become continuous ones. 相似文献
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A computational algorithm for solving a class of optimal control problems involving terminal and continuous state constraints of inequality type was developed in Ref. 1. In this paper, we extend the results of Ref. 1 to a more general class of constrained time-delayed optimal control problems, which involves terminal state equality constraints as well as terminal state inequality constraints and continuous state constraints. Two examples have been solved to illustrate the efficiency of the method. 相似文献
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The existence of continuous positional strategies of ?-optimal feedback is proved for linear optimal control problems with a convex terminal cost. These continuous feedbacks are determined from Bellman's equation in ?-perturbed control problems with an integral-terminal cost and a smooth value function. An example is given in which an ?-optimal continuous feedback does not exist. It is shown that the point limit of the ?-optimal feedbacks when ?→0 determines the optimal feedback, that is, a positional strategy and, possibly, a discontinuous strategy. 相似文献
19.
We consider optimal control problems with distributed control that involve a time-stepping formulation of dynamic one body contact problems as constraints. We link the continuous and the time-stepping formulation by a nonconforming finite element discretization and derive existence of optimal solutions and strong stationarity conditions. We use this information for a steepest descent type optimization scheme based on the resulting adjoint scheme and implement its numerical application. 相似文献
20.
Maurice Robin 《Acta Appl Math》1983,1(3):281-299
This paper addresses the long-term average cost control of continuous time Markov processes. A survey of problems and methods contained in various works is given for continuous control, optimal stopping, and impulse control. 相似文献