共查询到20条相似文献,搜索用时 109 毫秒
1.
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
2.
V. V. Ternovskii M. M. Khapaev 《Moscow University Computational Mathematics and Cybernetics》2010,34(2):97-99
An algorithm for numerically solving optimal control problems by methods applied to ill-posed problems is discussed. The stable
algorithms for solving such problems on compact sets developed by Academician A.N. Tikhonov in the twentieth century can be
applied to problems of optimal control. The special feature of optimal control problems is the discontinuity of a control
function. This difficulty is overcome by introducing a moving computational grid. The step size of the grid is determined
by solving the speed problem. 相似文献
3.
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
4.
Daim-Yuang Sun Sheng-Chung Ni Tzu-Chen Huang 《Applied mathematics and computation》2010,216(11):3343-3354
In this study, a modified line-up competition algorithm (LCA) is used to solve parameter selection problems. The so-called parameter selection problems contain parameter identification problems and optimal control problems. Once the later problems are transformed by control parametrization, the parameters embedded in both problems are selected by the proposed method under the framework of integration approach. Two parameter identification problems and one optimal control problem are given to demonstrate the use of LCA. The results show that in addition to being insensitive to the initial conditions, LCA is very efficient in solving highly nonlinear parameter selection problems. 相似文献
5.
A modified multiplier method for optimization problems with equality constraints is suggested and its application to constrained optimal control problems described. For optimal control problems with free terminal time, a gradient descent technique for updating control functions as well as the terminal time is developed. The modified multiplier method with the simplified conjugate gradient method is used to compute the solution of a time-optimal control problem for a V/STOL aircraft. 相似文献
6.
Extremum principles intended for use in optimal control are derived in the form of necessary conditions and sufficient conditions, formulated in general normed linear spaces. The method of application is illustrated by several examples involving optimal control problems, mathematical programming problems, lumped-parameter systems, and distributed-parameter systems. The basic theorems provide a unified approach which is applicable to a wide variety of problems in open-loop optimal control. 相似文献
7.
Jean-Michel Bismut 《Journal of Functional Analysis》1981,42(2):226-270
The purpose of this paper is to show the relation between the search for the minimal solution of certain systems of convex inequalities in potential theory and the solution of a very large class of stochastic control problems. Special attention is given to the control of alternating processes, and impulse control problems. The dual problems—in the sense of convex programming—are studied as well; and their solutions are interpreted in the framework of stochastic control theory. 相似文献
8.
A theorem on error estimates for smooth nonlinear programming problems in Banach spaces is proved that can be used to derive optimal error estimates for optimal control problems. This theorem is applied to a class of optimal control problems for quasilinear elliptic equations. The state equation is approximated by a finite element scheme, while different discretization methods are used for the control functions. The distance of locally optimal controls to their discrete approximations is estimated. 相似文献
9.
Xinwei Feng 《Stochastics An International Journal of Probability and Stochastic Processes》2016,88(8):1188-1206
This paper is concerned with the stochastic maximum principle for impulse optimal control problems of forward–backward systems, where the coefficients of the forward part are Lipschitz continuous. The domain of the regular controls is not necessarily convex. We establish a Pontryagins maximum principle for this control problem by applying Ekelands variational principle to a sequence of approximated control problems with smooth coefficients of the initial problems. 相似文献
10.
The problem of optimal control of nonlinear control and state constrained control problems, where the state constraint may involve differential operators and the cost functionals may be nonsmooth, is studied. For this class of problems, necessary optimality conditions using techniques from infinite dimensional optimization theory adapted to the framework of control problems are derived. It is shown that the underlying structure admits a considerable relaxation of the classical constraint qualifications. The theory then is applied to examples of various nonlinear elliptic equations and state constraints. 相似文献
11.
A. Y. Azimov 《Journal of Optimization Theory and Applications》2008,137(1):61-74
The duality of multiobjective problems is studied with the help of the apparatus of conjugate set-valued mappings introduced
by the author. In this paper (Part 1), a duality theory is developed for set-valued mappings, which is then used to derive
dual relations for some general multiobjective optimization problems which include convex programming and optimal control
problems. Using this result, in the companion paper (Part 2), duality theorems are proved for multiobjective quasilinear and
linear optimal control problems. The theory is applied to get dual relations for some multiobjective optimal control problem. 相似文献
12.
13.
《Numerical Functional Analysis & Optimization》2013,34(7-8):973-990
A family of parameter dependent optimal control problems for nonlinear ODEs is considered. The problems are subject to pointwise control constraints. It is shown that the standard conditions, used in stability analysis of optimal control problems, ensure not only Lipschitz continuity, but also Bouligand differentiability of the solutions with respect to the parameter. The Bouligand differentials are characterized as the solutions to the accessory linear-quadratic optimal control problems. 相似文献
14.
Hongguo Xu 《Linear algebra and its applications》2006,414(1):97-124
We study two matrix pencils that arise, respectively, in discrete-time and continuous-time optimal and robust control. We introduce a one-to-one transformation between these two pencils. We show that for the pencils under the transformation, their regularity is preserved and their eigenvalues and deflating subspaces are equivalently related. The eigen-structures of the pencils under consideration have strong connections with the associated control problems. Our result may be applied to connect the discrete-time and continuous-time control problems and eventually lead to a unified treatment of these two types of control problems. 相似文献
15.
The solution methods for optimal control problems with coupled partial differential equations as constraints are computationally costly and memory intensive; in particular for problems stated on networks, this prevents the methods from being relevant. We present instantaneous control problems for the optimization of traffic flow problems on road networks. We derive the optimality conditions, investigate the relation to the full optimal control problem and prove that certain properties of the optimal control problem carry over to the instantaneous one. We propose a solution algorithm and compare quality of the computed controls and run‐times. Copyright © 2006 John Wiley & Sons, Ltd. 相似文献
16.
In this paper, we consider problems of optimal control involving stressed or strained states of orthotropic, noncircular cylindrical shells. It is assumed that the thickness of the shell is variable. The thickness and the radius of curvature of the directrix of the shell are assumed to be the controls. Existence of solutions for the optimal control problems considered is shown. In particular, existence of solutions for the problem of the minimal weight shell and the problem of nearest-to-equal-strength shell is shown. We present results on the approximation of the optimal control problems by a sequence of finite-dimensional problems, which may be reduced to nonlinear programming problems. 相似文献
17.
The paper concerns a numerical study of the performance of an approximate algorithm for convex stochastic control problems that was derived in a recent paper by two of the authors and is inspired by work done in the area of Stochastic Programming in connection with the Edmundson-Madansky inequality. The accuracy of the approximations is numerically tested by applying the algorithm to two classical convex stochastic control problems for which the optimal solution is known, namely the linear-quadratic and the inventory control problems. 相似文献
18.
The concept of a K-gradient, introduced in Ref. 1 in order to generalize the concept of a derived convex cone defined by Hestenes, is extended to weak multiobjective optimization problems including not only a state variable, but also a control variable. The new concept is employed to state multiplier rules for the local solutions of such dynamic multiobjective optimization problems. An application of these multiplier rules to the local solutions of an abstract multiobjective optimal control problem yields general necessary optimality conditions that can be used to derive concrete maximum principles for multiobjective optimal control problems, e.g., problems described by integral equations with additional functional constraints. 相似文献
19.
The purpose of the present work is to implement well-known statistical decision and game theory strategies into multiobjective
stochastic control problems of fluid dynamics. Such goal is first justified by the fact that deterministic (either singleobjective
or multiobjective) control problems that are obtained without taking into account the uncertainty of the model are usually
unreliable. Second, in most real-world problems, several goals must be satisfied simultaneously to obtain an optimal solution
and, as a consequence, a multiobjective control approach is more appropriate. Therefore, we develop a multiobjective stochastic
control algorithm for general fluid dynamics applications, based on the Bayes decision, adjoint formulation and the Nash equilibrium
strategies. The algorithm is exemplified by the multiobjective stochastic control of a periodic Burgers equation. 相似文献
20.
We consider optimal control problems with constraints at intermediate points of the trajectory. A natural technique (propagation
of phase and control variables) is applied to reduce these problems to a standard optimal control problem of Pontryagin type
with equality and inequality constraints at the trajectory endpoints. In this way we derive necessary optimality conditions
that generalize the Pontryagin classical maximum principle. The same technique is applied to so-called variable structure
problems and to some hybrid problems. The new optimality conditions are compared with the results of other authors and five
examples illustrating their application are presented. 相似文献