首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 46 毫秒
1.
We consider the problem on the optimal boundary control of string vibrations by a displacement at one endpoint of the string with the other endpoint being fixed. The problem is studied in the space   相似文献   

2.
We are the first solve the optimization problem for a boundary displacement control of string vibrations at one endpoint in the case of a nonstationary boundary condition containing a directional derivative at the other endpoint.  相似文献   

3.
We study a problem of optimal boundary control of vibrations of a one-dimensional elastic string, the objective being to bring the string from an arbitrary initial state into an arbitrary terminal state. The control is by the displacement at one end of the string, and a homogeneous boundary condition containing the time derivative is posed at the other end. We study the corresponding initial-boundary value problem in the sense of a generalized solution in the Sobolev space and prove existence and uniqueness theorems for the solution. An optimal boundary control in the sense of minimization of the boundary energy is constructed in closed analytic form.  相似文献   

4.
We consider four mixed problems for the string vibration equation with zero initial conditions, with a Bitsadze–Samarskii boundary condition of the general form at the right endpoint, and with an inhomogeneous Neumann or Dirichlet condition at the left endpoint. We prove the uniqueness of a generalized solution (in the sense of Il’in) of these problems and obtain an analytic representation of these solutions. The solution of each of the problems is represented in the form of a linear combination of functions constructed from the problem data, and recursion formulas for the coefficients of this linear combination are obtained.  相似文献   

5.
The problem of optimal boundary control by displacement at one end of a string under a specified force mode at the other end is studied in the sense of a generalized solution of the corresponding mixed initial-boundary value problem from a Sobolev space. The problem of choosing an optimal boundary control from an infinite number of admissible controls is solved. A generalized solution of the mixed initial-boundary value problem is constructed explicitly and the uniqueness of the solution is proved.  相似文献   

6.
We solve the problem of optimal boundary force control at one end of a string for the case of a given displacement mode at the other end. The problem is studied in the sense of a generalized solution of the corresponding mixed initial-boundary value problem in the Sobolev space. We also solve the problem of choosing an optimal boundary control from infinitely many feasible controls. The generalized solution of the mixed initial-boundary value problem is constructed in closed form, and the uniqueness of the solution is proved.  相似文献   

7.
We find necessary and sufficient conditions for the existence of a boundary control of vibrations of a string or a spherical layer for critical and subcritical times. We completely analyze the existence of a boundary control of vibrations of a spherical layer by a force on two spheres. We find necessary and sufficient existence conditions for the control. Along with the control problem for vibrations of a spherical layer, we consider a similar control problem for string vibrations.  相似文献   

8.
We consider the optimal boundary control of string vibrations and study the case of boundary force control at one end of the string, the other end being free. We show that if the initial and terminal data are arbitrary, then the dependence of the optimal boundary control on these data may be nonlinear. Conditions under which the dependence is linear are indicated. An example is considered in which the optimal control can be found in closed form.  相似文献   

9.
We consider the optimization problem for a nonlocal boundary control of vibrations of an elastic string with fixed right end for an arbitrary sufficiently large time interval that is a multiple of twice the string length. We prove the existence and uniqueness of a generalized solution of the first boundary value problem and indicate an explicit expression for the solution. The optimal control is found in closed form.  相似文献   

10.
We study the behavior of a string with the nonlocal boundary condition u x (l, t) = u x ($ x^\circ $ x^\circ , t). A displacement control u(0, t) = μ(t) bringing the string from an arbitrarily given initial state to an arbitrarily given terminal state is applied at the left endpoint of the string. For the initial and terminal functions, we find necessary and sufficient conditions for the controllability of the string. Under these conditions, we carry out optimization; i.e., of all admissible controls, we choose a control minimizing the boundary energy integral.  相似文献   

11.
An explicit analytic expression is obtained for optimal boundary controls exercised on one end of a string by a displacement or by an elastic force under a model nonlocal boundary condition of one of four types.  相似文献   

12.
An explicit analytic expression is obtained for optimal boundary controls exercised on one end of a string by a displacement or by an elastic force under a model nonlocal boundary condition of one of four types.  相似文献   

13.
We consider the problem of boundary control by a force applied to one end of a string in the case of a given force mode at the other end. The problem is studied in the sense of the generalized solution of the corresponding mixed initial-boundary value problem in the Sobolev space. We also solve the problem of choosing an optimal boundary control in the set of all admissible controls. The generalized solution of the mixed initial-boundary value problem is constructed in closed form, and its uniqueness is proved.  相似文献   

14.
We consider an optimal boundary control of a string with free end by a displacement of the other end in W p (Q, T). For p ≠ 2, we prove that the optimal control depends on the initial and terminal conditions nonlinearly.  相似文献   

15.
In this paper, we shall address three problems arising in the computation of eigenvalues of Sturm-Liouville boundary value problems. We first consider a well-posed Sturm-Liouville problem with discrete and distinct spectrum. For this problem, we shall show that the eigenvalues can be computed by solving for the zeros of the boundary condition at the terminal point as a function of the eigenvalue. In the second problem, we shall consider the case where some coefficients and parameters in the differential equation are continuously adjustable. For this, the eigenvalues can be optimized with respect to these adjustable coefficients and parameters by reformulating the problem as a combined optimal control and optimal parameter selection problem. Subsequently, these optimized eigenvalues can be computed by using an existing optimal control software, MISER. The last problem extends the first to nonstandard boundary conditions such as periodic or interrelated boundary conditions. To illustrate the efficiency and the versatility of the proposed methods, several non-trivial numerical examples are included.  相似文献   

16.
In the present paper, in terms of a generalized solution of the wave equation, we perform an exhaustive study of the problem on the boundary control by an elastic force u x (0, t) = µ(t) at one endpoint x = 0 of a string in the presence of a model nonlocal boundary condition of one of four types relating (with the sign “+” or “?”) the values of the displacement u(x, t) or its derivative u x (x, t) at the boundary point x = l of the string to their values at some interior point \(\mathop x\limits^ \circ \) of the string (0 < \(\mathop x\limits^ \circ \) < l). We prove necessary and sufficient conditions for the existence of such boundary controls. Under these conditions, we optimize the controls by minimizing the boundary energy integral and then write out the optimal boundary controls in closed analytic form.  相似文献   

17.
In the present paper, we consider a boundary control by displacements at one endpoint of an inhomogeneous rod that has two parts of different densities and elasticities with fixed other endpoint for the case in which the times of passage of the wave through each of these inhomogeneity parts coincide. We find a closed analytic form of the boundary control by displacements bringing the stick from the original rest state into a given terminal state specified by given terminal displacement and velocity.  相似文献   

18.
We consider the minimization problem for the energy functional of a two-phase medium concentrated at the boundary of a domain. We study regularization of the functional by means of the area of the boundary of the phase interface under additional conditions on the displacement field. Bibliography: 3 titles.  相似文献   

19.
We consider control problems for the 3D Maxwell equations describing electromagnetic wave scattering in an unbounded inhomogeneous medium that contains a permeable isotropic obstacle with cloaking boundary. Such problems arise when studying cloaking problems by the optimization method. The boundary coefficient occurring in the impedance boundary condition plays the role of a control. We study the solvability of the control problem and derive optimality systems that describe necessary conditions for the extremum. By analyzing the constructed optimality systems, we justify sufficient conditions imposed on the input data providing the uniqueness and stability of optimal solutions.  相似文献   

20.
This paper is concerned with a one-dimensional vibrating string equation with a nonlinear boundary condition at one endpoint. By applying the snap-back repeller theory, the gradient of the wave equation is proved to be chaotic in the sense of both Devaney and Li-Yorke under some conditions. In addition, an illustrative example is provided with computer simulations.  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号