共查询到20条相似文献,搜索用时 78 毫秒
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本文对于Banach空间中分布参数系统讨论非光滑指标奇异最优控制问题,利用Moors-Penrose广义逆与Clarke广义梯度证得奇异最优控制的存在性,并给出广义一阶必要条件,推广了Lions[3]的相应结果. 相似文献
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周渊 《数学年刊A辑(中文版)》1991,(6)
本文考虑Hilbert空间上线性二次最优控制问题,其中的二次指标可以是奇异的。本文讨论了最优控制问题的适定性和可解性并给出了频率判据,在一定条件下得到了闭环最优解,最后对有限维情况给出了更强的结果。 相似文献
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陈莉 《高校应用数学学报(A辑)》2007,22(1):9-16
研究了非方广义系统带最坏干扰抑制的奇异线性二次指标最优控制问题(即LQ问题).在给定的条件下,最坏干扰和最优控制—状态对均存在且惟一,最优控制可被综合为状态反馈.在最坏干扰和最优控制作用下,所得闭环系统的任意有限特征值均在开左半复平面,且闭环系统的状态有最少自由元. 相似文献
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研究了奇异齐次非线性系统的最优控制问题与相关的L2增益问题,基于Hamilton-Jacobi不等式,我们给出了可解性条件,并显式构造出了控制律,在保证内稳定的基础上达到干扰衰减. 相似文献
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通过在目标结构中引入收益率及破产补偿函数,建立了一非对称型最优奇异随机控制模型.利用随机积分及最优控制理论,得出了最大回报函数的显式解及相应的最优控制策略. 相似文献
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本文介绍了由偏微分方程支配的系统的最优控制理论中有关应用奇异摄动方法时出现的各种问题。考虑了渐近分析来自状态方程。或来自性能指标函数,也考虑了状态方程是定义在摄动域内的情形。 相似文献
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以随机分析的知识和最优控制理论为基础,讨论了一类带停时的奇异型随机控制的折扣费用模型,在原模型的状态过程的基础上添加了漂移因子和扩散因子,并在λ<δα的情况下讨论了该问题相应的变分方程的解,给出了此随机控制问题的最优策略,即最优控制和最优停时,并且证明了变分方程的解即为最优费用函数. 相似文献
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A. Yu. Chebotarev 《Differential Equations》2010,46(12):1779-1785
We consider optimal control problems for stationary systems whose solutions are unstable singular points of the corresponding
evolution equations. We suggest a construction of a feedback control stabilizing the optimal state. 相似文献
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H. L. Stalford F. E. Garrett Jr. 《Journal of Optimization Theory and Applications》1994,80(2):227-260
The Frenet-Serret equations of classical differential geometry are used to describe the quickest descent tunneling path problem. The optimal tunnel is shown to have a constant turn rate with zero torsion and is equivalent to Edelbaum's hypocycloid solution. The solutions are obtained using the maximum principle and singular arc conditions. The optimal curvature is a first-order singular arc and the optimal torsion is a second-order singular arc. Our treatment includes both the normal and the abnormal optimal control problems. Our problem is abnormal for the case where the final speed is zero. Analytical solutions for the optimal time histories are derived for all states and all adjoint states. One of Leitmann's sufficiency field theorems is used to establish optimality of the solutions. 相似文献
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Tien Dung Nguyen 《Applications of Mathematics》2016,61(5):515-526
Stochastic Riccati equation is a backward stochastic differential equation with singular generator which arises naturally in the study of stochastic linear-quadratic optimal control problems. In this paper, we obtain Gaussian density estimates for the solutions to this equation. 相似文献
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A numerical method is proposed for constructing an approximation of the Pareto front of nonconvex multi-objective optimal control problems. First, a suitable scalarization technique is employed for the multi-objective optimal control problem. Then by using a grid of scalarization parameter values, i.e., a grid of weights, a sequence of single-objective optimal control problems are solved to obtain points which are spread over the Pareto front. The technique is illustrated on problems involving tumor anti-angiogenesis and a fed-batch bioreactor, which exhibit bang–bang, singular and boundary types of optimal control. We illustrate that the Bolza form, the traditional scalarization in optimal control, fails to represent all the compromise, i.e., Pareto optimal, solutions. 相似文献
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Hans Joachim Oberle 《Applied Mathematics and Optimization》1979,5(1):297-314
The method presented here is an extension of the multiple shooting algorithm in order to handle multipoint boundary-value problems and problems of optimal control in the special situation of singular controls or constraints on the state variables. This generalization allows a direct treatment of (nonlinear) conditions at switching points. As an example a model of optimal heating and cooling by solar energy is considered. The model is given in the form of an optimal control problem with three control functions appearing linearly and a first order constraint on the state variables. Numerical solutions of this problem by multiple shooting techniques are presented. 相似文献
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W. F. Powers 《Journal of Optimization Theory and Applications》1980,32(4):479-489
In singular optimal control problems, the functional form of the optimal control function is usually determined by solving the algebraic equation which results by successively differentiating the switching function until the control appears explicitly. This process defines the order of the singular problem. Order-related results are developed for singular linear-quadratic problems and for a bilinear example which gives new insights into the relationship between singular problem order and singular are order.Dedicated to R. BellmanThis work was supported by the National Science Foundation under Grant No. ENG-77-16660. 相似文献
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Z. A. Tsintsadze 《Journal of Mathematical Sciences》2008,148(3):399-480
The paper elaborates a general method for studying smooth-convex conditional minimization problems that allows one to obtain
necessary conditions for solutions of these problems in the case where the image of the mapping corresponding to the constraints
of the problem considered can be of infinite codimension.
On the basis of the elaborated method, the author proves necessary optimality conditions in the form of an analog of the Pontryagin
maximum principle in various classes of quasilinear optimal control problems with mixed constraints; moreover, the author
succeeds in preserving a unified approach to obtaining necessary optimality conditions for control systems without delays,
as well as for systems with incommensurable delays in state coordinates and control parameters. The obtained necessary optimality
conditions are of a constructive character, which allows one to construct optimal processes in practical problems (from biology,
economics, social sciences, electric technology, metallurgy, etc.), in which it is necessary to take into account an interrelation
between the control parameters and the state coordinates of the control object considered. The result referring to systems
with aftereffect allows one to successfully study many-branch product processes, in particular, processes with constraints
of the “bottle-neck” type, which were considered by R. Bellman, and also those modern problems of flight dynamics, space navigation,
building, etc. in which, along with mixed constraints, it is necessary to take into account the delay effect.
The author suggests a general scheme for studying optimal process with free right endpoint based on the application of the
obtained necessary optimality conditions, which allows one to find optimal processes in those control systems in which no
singular cases arise.
The author gives an effective procedure for studying the singular case (the procedure for calculating a singular control in
quasilinear systems with mixed constraints.
Using the obtained necessary optimality conditions, the author constructs optimal processes in concrete control systems.
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 42, Optimal
Control, 2006. 相似文献
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A reproducing kernel method is proposed to obtain the optimal and approximate solutions of Carleman singular integral equations. Therefore, we will be mostly interested in singular integral equations with a Cauchy type kernel and whose coefficients are real or complex valued functions. The new method and corresponding concepts allow the analysis of associated discrete singular integral equations and corresponding inverse source problems in appropriate frameworks. 相似文献
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This article studies singular mean field control problems and singular mean field two-players stochastic differential games. Both sufficient and necessary conditions for the optimal controls and for the Nash equilibrium are obtained. Under some assumptions the optimality conditions for singular mean-field control are reduced to a reflected Skorohod problem, whose solution is proved to exist uniquely. Motivations are given as optimal harvesting of stochastic mean-field systems, optimal irreversible investments under uncertainty and mean-field singular investment games. In particular, a simple singular mean-field investment game is studied, where the Nash equilibrium exists but is not unique. 相似文献
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We consider a family of parametric linear-quadratic optimal control problems with terminal and control constraints. This family has the specific feature that the class of optimal controls is changed for an arbitrarily small change in the parameter. In the perturbed problem, the behavior of the corresponding trajectory on noncritical arcs of the optimal control is described by solutions of singularly perturbed boundary value problems. For the solutions of these boundary value problems, we obtain an asymptotic expansion in powers of the small parameter ?. The asymptotic formula starts from a term of the order of 1/? and contains boundary layers. This formula is used to justify the asymptotic expansion of the optimal control for a perturbed problem in the family. We suggest a simple method for constructing approximate solutions of the perturbed optimal control problems without integrating singularly perturbed systems. The results of a numerical experiment are presented. 相似文献