共查询到20条相似文献,搜索用时 0 毫秒
1.
A. J. Zaslavski 《Journal of Optimization Theory and Applications》2010,145(3):597-612
We study the structure of solutions of a discrete-time control system with a compact metric space of states X which arises in economic dynamics. This control system is described by a nonempty closed set Ω⊂X×X which determines a class of admissible trajectories (programs) and by a bounded upper semicontinuous objective function v:Ω→R
1 which determines an optimality criterion. We are interested in turnpike properties of the approximate solutions which are
independent of the length of the interval, for all sufficiently large intervals. In the present paper, we show that these
turnpike properties are stable under perturbations of the objective function v. 相似文献
2.
The finite difference method is applied to an optimal control problem for a system governed by a nonlinear Schrödinger equation with a complex coe?cient. The optimal control problem is discretized by the finite difference method, the error estimate for the finite difference scheme is established and the convergence of difference approximations of the optimal control according to the functional is proved. 相似文献
3.
4.
In this article, we deal with a control problem for a singular system regarding a phase-field model which describes a solid–liquid transition by the Ginzburg–Landau theory. The purpose is to control the system by the means of the heat supply r able to guide it into a certain state with a solid (or liquid) part in a prescribed subset Ω0 of the space domain Ω, and maintain it in this state during a period of time. The transition is described by a nonlinear differential system of two equations for the phase field and temperature. The control problem is set for some expressions of the cost functional which might reveal cases of physical interest. An approximating control problem is introduced and the existence of at least an optimal pair is proved. The first-order optimality conditions for the approximating problem are determined and a convergence result is given. 相似文献
5.
Chun-fa Li Xue Yang En-min Feng 《应用数学学报(英文版)》2008,24(1):29-40
In this paper, an optimal control problem governed by semilinear parabolic equation which involves the control variable acting on forcing term and coefficients appearing in the higher order derivative terms is formulated and analyzed. The strong variation method, due originally to Mayne et al to solve the optimal control problem of a lumped parameter system, is extended to solve an optimal control problem governed by semilinear parabolic equation, a necessary condition is obtained, the strong variation algorithm for this optimal control problem is presented, and the corresponding convergence result of the algorithm is verified. 相似文献
6.
Chao-hua Jia De-xing Feng 《应用数学学报(英文版)》2007,23(3):377-388
An optimal control problem for a coupled nonlinear parabolic population system is considered. The existence and uniqueness of the positive solution for the system is shown by the method of upper and lower solutions. An explicit prior bound of solutions to the system is given by considering an auxiliary coupled linear system. The existence of the optimal control is proved and the characterization of the optimal control is established. 相似文献
7.
Brizitskii R. V. Saritskaya Zh. Yu. 《Computational Mathematics and Mathematical Physics》2018,58(12):2053-2063
Computational Mathematics and Mathematical Physics - The solvability of boundary-value and extremum problems for a nonlinear convection–diffusion–reaction equation with mixed boundary... 相似文献
8.
Ukrainian Mathematical Journal - We study the problem of existence and uniqueness of the solution of a three-point boundary-value problem for a differential equation of fractional order. Further,... 相似文献
9.
There are very few results about analytic solutions of problems of optimal control with minimal L
norm. In this paper, we consider such a problem for the wave equation, where the derivative of the state is controlled at both boundaries. We start in the zero position and consider a problem of exact control, that is, we want to reach a given terminal state in a given finite time. Our aim is to find a control with minimal L
norm that steers the system to the target.We give the analytic solution for certain classes of target points, for example, target points that are given by constant functions. For such targets with zero velocity, the analytic solution has been given by Bennighof and Boucher in Ref. 1. 相似文献
10.
AbdulRahman Al-Hussein 《Applied Mathematics and Optimization》2011,63(3):385-400
We consider a nonlinear stochastic optimal control problem associated with a stochastic evolution equation. This equation
is driven by a continuous martingale in a separable Hilbert space and an unbounded time-dependent linear operator. 相似文献
11.
Imran H. Biswas Espen R. Jakobsen Kenneth H. Karlsen 《Applied Mathematics and Optimization》2010,62(1):47-80
We develop a viscosity solution theory for a system of nonlinear degenerate parabolic integro-partial differential equations
(IPDEs) related to stochastic optimal switching and control problems or stochastic games. In the case of stochastic optimal
switching and control, we prove via dynamic programming methods that the value function is a viscosity solution of the IPDEs.
In our setting the value functions or the solutions of the IPDEs are not smooth, so classical verification theorems do not
apply. 相似文献
12.
Lingeshwaran Shangerganesh Puthur Thangaraj Sowndarrajan 《Numerical Functional Analysis & Optimization》2013,34(14):1574-1593
AbstractAn optimal control problem constrained by a reaction–diffusion mathematical model which incorporates the cancer invasion and its treatment is considered. The state equations consisting of three unknown variables namely tumor cell density, normal cell density, and drug concentration. The main goal of the considered optimal control problem is to minimize the density of cancer cells and decreasing the side effects of treatment. Moreover, existence of a weak solution of brain tumor reaction–diffusion system and the corresponding adjoint system of optimal control problem is also investigated. Further, existence of minimizer for the optimal control problem is established and also the first-order optimality conditions are derived. 相似文献
13.
《数学研究与评论》1983,(3)
Lyapunov's second method in fact is that which may be described as follows:applying the comparison principle to the V-function, we may render the stability ofthe solution of a vector differential.equation to that of the scalar differential equation du/dt=ω(t,u),ω(t,0)≡0,0≤u≤ρ(t),t∈ [cf. C. Corduneanu, 1960]. Unfortunately, the stability of the solutions of scalardifferential equations had not been well-discussed. In literatures, ρ is assumed to be 相似文献
14.
First we establish a Carleman estimate for Lotka-Volterra competition-diffusion system of three equations with variable coefficients.
Then the internal observations with two measurements are allowed to obtain the stability result for the inverse problem consisting
of retrieving two smooth diffusion coefficients in the given parabolic system for the dimension n≤3. The proof of the results rely on Carleman estimates and certain energy estimates for parabolic system. 相似文献
15.
In this note, we investigate upper bounds of the Neumann eigenvalue problem for the Laplacian of a domain Ω in a given complete
(not compact a priori) Riemannian manifold (M,g). For this, we use test functions for the Rayleigh quotient subordinated to a family of open sets constructed in a general
metric way, interesting for itself. As applications, we prove that if the Ricci curvature of (M,g) is bounded below Ric
g
≥−(n−1)a
2, a≥0, then there exist constants A
n
>0,B
n
>0 only depending on the dimension, such that
where λ
k
(Ω) (k∈ℕ*) denotes the k-th eigenvalue of the Neumann problem on any bounded domain Ω⊂M of volume V=Vol (Ω,g). Furthermore, this upper bound is clearly in agreement with the Weyl law. As a corollary, we get also an estimate which
is analogous to Buser’s upper bounds of the spectrum of a compact Riemannian manifold with lower bound on the Ricci curvature.
相似文献
16.
XiaoFengLIU YongYangJIN 《数学学报(英文版)》2005,21(2):393-408
We consider the Cauchy problem of a shallow water equation and its local wellposedness. 相似文献
17.
This paper is devoted to the analysis of a bilinear optimal control problem subject to the Fokker–Planck equation. The control function depends on time and space and acts as a coefficient of the advection term. For this reason, suitable integrability properties of the control function are required to ensure well posedness of the state equation. Under these low regularity assumptions and for a general class of objective functionals, we prove the existence of optimal controls. Moreover, for common quadratic cost functionals of tracking and terminal type, we derive the system of first-order necessary optimality conditions. 相似文献
18.
Equations for the Missing Boundary Values in the Hamiltonian Formulation of Optimal Control Problems
Vicente Costanza Pablo S. Rivadeneira Ruben D. Spies 《Journal of Optimization Theory and Applications》2011,149(1):26-46
Partial differential equations for the unknown final state and initial costate arising in the Hamiltonian formulation of regular
optimal control problems with a quadratic final penalty are found. It is shown that the missing boundary conditions for Hamilton’s
canonical ordinary differential equations satisfy a system of first-order quasilinear vector partial differential equations
(PDEs), when the functional dependence of the H-optimal control in phase-space variables is explicitly known. Their solutions are computed in the context of nonlinear systems
with ℝ
n
-valued states. No special restrictions are imposed on the form of the Lagrangian cost term. Having calculated the initial
values of the costates, the optimal control can then be constructed from on-line integration of the corresponding 2n-dimensional Hamilton ordinary differential equations (ODEs). The off-line procedure requires finding two auxiliary n×n matrices that generalize those appearing in the solution of the differential Riccati equation (DRE) associated with the linear-quadratic
regulator (LQR) problem. In all equations, the independent variables are the finite time-horizon duration T and the final-penalty matrix coefficient S, so their solutions give information on a whole two-parameter family of control problems, which can be used for design purposes.
The mathematical treatment takes advantage from the symplectic structure of the Hamiltonian formalism, which allows one to
reformulate Bellman’s conjectures concerning the “invariant-embedding” methodology for two-point boundary-value problems.
Results for LQR problems are tested against solutions of the associated differential Riccati equation, and the attributes
of the two approaches are illustrated and discussed. Also, nonlinear problems are numerically solved and compared against
those obtained by using shooting techniques. 相似文献
19.
In this paper we study the asymptotic behavior of a system modeling heating of material by microwaves. Various assumptions have been made, concerning complexity (nonhomogeneous structure) and the two-phase state of the material. The mathematical model includes Maxwell’s and heat–transfer equations. Stability of solutions of the system is shown. 相似文献
20.
Sh. M. Nasibov 《Theoretical and Mathematical Physics》2018,195(2):658-664
We study the problem of the absence of global solutions of the first mixed problem for one nonlinear evolution equation of Schrödinger type. We prove that global solutions of the studied problem are absent for “sufficiently large” values of the initial data. 相似文献