共查询到9条相似文献,搜索用时 15 毫秒
1.
A. V. Belikov 《Differential Equations》2013,49(11):1336-1346
We study a boundary displacement control at two ends of an inhomogeneous rod that has two parts of distinct densities and elasticities in the case of coinciding wave propagation times over these parts. The control acts on a time interval of critical length. We obtain a closed analytical form of the boundary displacement control bringing the rod in critical time from the initial state of rest into a given terminal state specified by given terminal displacement and terminal velocity. 相似文献
2.
A. V. Belikov 《Differential Equations》2011,47(3):402-411
We study the boundary control by an elastic force at one end of an inhomogeneous rod that has two parts of different densities
and elasticities and whose other end is free. The case in which the wave travels either of the homogeneous parts in the same
time is considered. We present a closed-form analytical expression for the boundary control by an elastic force that brings
the rod from the initial quiescent state to a given terminal state specified by given terminal displacement and terminal velocity. 相似文献
3.
A. V. Belikov 《Differential Equations》2010,46(8):1178-1187
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
4.
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
$$u_{tt} (x,t) - u_{tt} (x,t) = 0,$$
$$\{ u(x,0) = \varphi (x), u_t (x,0) = \psi (x)$$
$$\{ u(x,T) = \hat \varphi (x), u_t (x,T) = \hat \psi (x).$$
5.
A. M. Rogozhnikov 《Differential Equations》2013,49(5):607-616
We consider longitudinal elastic vibrations of a composite rod and find closedform expressions that describe optimal boundary controls bringing the rod from the quiescent state into a state with given displacement function φ(t) and velocity function ψ(t) in time T. We assume that the wave propagation time through each part of the rod is the same and T is a multiple of that time. 相似文献
6.
Problems with one-sided boundary controls of three basic types and homogeneous boundary third conditions on uncontrollable ends are considered for a wave equation in classes of strong generalized solutions in time intervals of strict critical length. New constructive observability inequalities are obtained for dual problems in adjoint classes of weak generalized solutions. 相似文献
7.
8.
We consider a boundary value problem for the wave equation with given initial conditions and with boundary conditions of the second kind at one end of the string and boundary conditions of the first kind at the other end of the string. We assume the boundary conditions to ensure that the solution of the problem (in the class of generalized functions) satisfying the initial conditions at the initial time t = 0 satisfies given terminal conditions at the terminal time t = T. We clarify the relationship between the functions µ(t) and ν(t) in the boundary conditions and the given functions specifying the initial and terminal states. We obtain closed-form analytic expressions for the functions µ(t) and ν(t) minimizing the boundary energy functional. 相似文献
9.
V. A. Il’in 《Differential Equations》2009,45(4):602-611
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