共查询到20条相似文献,搜索用时 500 毫秒
1.
Yu. N. Kiselev M. V. Orlov 《Moscow University Computational Mathematics and Cybernetics》2011,35(4):159-166
A model of gas field development described as a nonlinear optimum control problem with an infinite planning horizon is considered.
The Pontryagin maximum principle is used to solve it. The theorem on sufficient optimumity conditions in terms of constructions
of the Pontryagin maximum principles is used to substantiate the optimumity of the extremal solution. A procedure for constructing
the optimum solution by dynamic programming is described and is of some methodological interest. The obtained optimum solution
is used to construct the Bellman function. Reference is made to a work containing an economic interpretation of the problem. 相似文献
2.
Martin Bohner Kenzhegaly Kenzhebaev Oleksandr Stanzhytskyi 《Journal of Difference Equations and Applications》2017,23(7):1161-1189
In this work, an analogue of Pontryagin’s maximum principle for dynamic equations on time scales is given, combining the continuous and the discrete Pontryagin maximum principles and extending them to other cases ‘in between’. We generalize known results to the case when a certain set of admissible values of the control is not necessarily closed (but convex) and the attainable set is not necessarily convex. At the same time, we impose an additional condition on the graininess of the time scale. For linear systems, sufficient conditions in the form of the maximum principle are obtained. 相似文献
3.
R. J. Hartberger 《Journal of Optimization Theory and Applications》1973,11(2):139-145
Many optimization problems in economic analysis, when cast as optimal control problems, are initial-value problems, not two-point boundary-value problems. While the proof of Pontryagin (Ref. 1) is valid also for initial-value problems, it is desirable to present the potential practitioner with a simple proof specially constructed for initial-value problems. This paper proves the Pontryagin maximum principle for an initial-value problem with bounded controls, using a construction in which all comparison controls remain feasible. The continuity of the Hamiltonian is an immediate corollary. The same construction is also shown to produce the maximum principle for the problem of Bolza. 相似文献
4.
By introducing the concept of a γ-convex set, a new discrete analogue of Pontryagin’s maximum principle is obtained. By generalizing the concept of the relative interior of a set, an equality-type optimality condition is proved, which is called by the authors the Pontryagin equation. 相似文献
5.
S. M. Aseev 《Proceedings of the Steklov Institute of Mathematics》2015,291(1):38-48
A class of infinite-horizon optimal control problems that arise in economic applications is considered. A theorem on the nonemptiness and boundedness of the set of optimal controls is proved by the method of finite-horizon approximations and the apparatus of the Pontryagin maximum principle. As an example, a simple model of optimal economic growth with a renewable resource is considered. 相似文献
6.
Differential Equations - We consider an iterative regularization of the classical optimality conditions—Lagrange’s principle and Pontryagin’s maximum principle—in a convex... 相似文献
7.
Backward stochastic Volterra integral equations (BSVIEs, for short) are introduced. The existence and uniqueness of adapted solutions are established. A duality principle between linear BSVIEs and (forward) stochastic Volterra integral equations is obtained. As applications of the duality principle, a comparison theorem is proved for the adapted solutions of BSVIEs, and a Pontryagin type maximum principle is established for an optimal control of stochastic integral equations. 相似文献
8.
In the present paper, we study the resource allocation problem for a two-sector economic model of special form, which is of
interest in applications. The optimization problem is considered on a given finite time interval. We show that, under certain
conditions on the model parameters, the optimal solution contains a singular mode. We construct optimal solutions in closed
form. The theoretical basis for the obtained results is provided by necessary optimality conditions (the Pontryagin maximum
principle) and sufficient optimality conditions in terms of constructions of the Pontryagin maximum principle. 相似文献
9.
Three optimal control problems involving measure functional differential equations are considered. The necessary conditions, in the form of the Pontryagin maximum principle, for an optimal control are obtained. This is accomplished by the application of a theorem by Debovistskii-Milyutin. A simple example is also illustrated to show the applicability of the results obtained. 相似文献
10.
Yu. N. Kiselev M. V. Orlov S. M. Orlov 《Moscow University Computational Mathematics and Cybernetics》2018,42(4):152-162
The classical two-dimensional Fuller problem is considered. The boundary value problem of Pontryagin’s maximum principle is considered. Based on the central symmetry of solutions to the boundary value problem, the Pontryagin maximum principle as a necessary condition of optimality, and the hypothesis of the form of the switching line, a solution to the boundary value problem is constructed and its optimality is substantiated. Invariant group analysis is in this case not used. The results are of considerable methodological interest. 相似文献
11.
12.
R. V. Gamkrelidze 《Proceedings of the Steklov Institute of Mathematics》2015,291(1):61-67
An invariant dual formulation of the Pontryagin maximum principle is given for the time-optimal case. 相似文献
13.
V. K. Bulgakov V. V. Strigunov 《Computational Mathematics and Mathematical Physics》2009,49(5):748-761
The Pontryagin maximum principle is used to prove a theorem concerning optimal control in regional macroeconomics. A boundary value problem for optimal trajectories of the state and adjoint variables is formulated, and optimal curves are analyzed. An algorithm is proposed for solving the boundary value problem of optimal control. The performance of the algorithm is demonstrated by computing an optimal control and the corresponding optimal trajectories. 相似文献
14.
We consider control systems in an abstract Banach space with control in the form of an operator function. For such systems,
we derive necessary optimality conditions in the form of the Pontryagin maximum principle. 相似文献
15.
16.
R. V. Gamkrelidze 《Proceedings of the Steklov Institute of Mathematics》2010,268(1):87-92
A basic feature of Pontryagin’s maximum principle is its native Hamiltonian format, inherent in the principle regardless of
any regularity conditions imposed on the optimal problem under consideration. It canonically assigns to the problem a family
of Hamiltonian systems, indexed with the control parameter, and complements the family with the maximum condition, which makes
it possible to solve the initial value problem for the system by “dynamically” eliminating the parameter as we proceed along
the trajectory, thus providing extremals of the problem. Much has been said about the maximum condition since its discovery
in 1956, and all achievements in the field were mainly credited to it, whereas the Hamiltonian format of the maximum principle
has always been taken for granted and never been discussed seriously. Meanwhile, the very possibility of formulating the maximum
principle is intimately connected with its native Hamiltonian format and with the parametrization of the problem with the
control parameter. Both these starting steps were made by L.S. Pontryagin in 1955 from scratch, in fact, out of nothing, and
eventually led to the discovery of the maximum principle. Since the present volume is dedicated to the centenary of the birth
of Lev Semenovich Pontryagin, I decided to return to this now semi-historical topic and give a short exposition of the Hamiltonian
format of the maximum principle. 相似文献
17.
M. I. Sumin 《Computational Mathematics and Mathematical Physics》2009,49(12):1987-2005
The perturbation method is used in the dual regularization theory for a linear convex optimal control problem with a strongly
convex objective functional and pointwise state constraints understood as ones in L
2. Primary attention is given to the qualitative properties of the dual regularization method, depending on the differential
properties of the value function (S-function) in the optimization problem. It is shown that the convergence of the method is closely related to the Lagrange
principle and the Pontryagin maximum principle. The dual regularization scheme is shown to provide a new method for proving
the maximum principle in the problem with pointwise state constraints understood in L
2 or C. The regularized Lagrange principle in nondifferential form and the regularized Pontryagin maximum principle are discussed.
Illustrative examples are presented. 相似文献
18.
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
19.
M. I. Sumin 《Proceedings of the Steklov Institute of Mathematics》2011,275(1):161-177
A problem of optimal boundary control is considered for a divergent linear parabolic equation. Equality constraints of the problem are given by nondifferentiable functionals. A dual regularization algorithm stable to errors in initial data is constructed for solving the problem. Pontryagin’s maximum principle plays the key role in this algorithm. 相似文献
20.
A. V. Arutyunov 《Differential Equations》2012,48(12):1586-1595
We study the Pontryagin maximum principle for an optimal control problem with state constraints. We analyze the continuity of a vector function µ (which is one of the Lagrange multipliers corresponding to an extremal by virtue of the maximum principle) at the points where the extremal trajectory meets the boundary of the set given by the state constraints. We obtain sufficient conditions for the continuity of µ in terms of the smoothness of the extremal trajectory. 相似文献