共查询到20条相似文献,搜索用时 62 毫秒
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E. I. Moiseev A. A. Kholomeeva 《Proceedings of the Steklov Institute of Mathematics》2012,276(1):153-160
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
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Optimal boundary force control at one end of a string for a given displacement mode at the other end
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
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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
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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
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M. F. Abdukarimov 《Differential Equations》2014,50(5):677-688
For a string vibration process described by an inhomogeneous wave equation, we consider the problem of boundary control at one end of the string with the other end being fixed. For any time interval T > 2l, where l is the string length, we find a function u(0, t) = µ(t) bringing the vibration system from a given initial state into a given terminal state and minimizing the boundary energy integral. 相似文献
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V. A. Il’in 《Proceedings of the Steklov Institute of Mathematics》2010,268(1):117-129
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
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We further develop the method, devised earlier by the authors, which permits finding closed-form expressions for the optimal controls by elastic boundary forces applied at two ends, x = 0 and x = l, of a string. In a sufficiently large time T, the controls should take the string vibration process, described by a generalized solution u(x, t) of the wave equation from an arbitrary initial state to an arbitrary terminal state
相似文献
$$u_{tt} (x,t) - u_{tt} (x,t) = 0,$$
$$\{ u(x,0) = \varphi (x), u_t (x,0) = \psi (x)$$
$$\{ u(x,T) = \hat \varphi (x), u_t (x,T) = \hat \psi (x).$$
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A. A. Nikitin 《Differential Equations》2011,47(12):1796-1805
We study a boundary control problem based on a mixed problem with an inhomogeneous condition of the second kind at the left
end of a string with elastically fixed right end. The difficulty in the solution of that problem is that the fixing condition
is absent. Therefore, in addition to a constraint that is an equality of functions in the class L
2, we need one more condition, to which V.A. Il’in refers as a condition of coordination of the initial and terminal displacements.
We develop a new optimization method based on the extension of the terminal conditions to the interval [−T,T]. This permits one to minimize the integral of the squared boundary control. A control minimizing this energy integral is
written out in closed form. 相似文献