共查询到20条相似文献,搜索用时 0 毫秒
1.
I. Sadek J. M. Sloss J. C. Bruch Jr. S. Adali 《Journal of Optimization Theory and Applications》1986,50(3):451-461
The present paper considers the problem of optimally controlling the deflections and/or velocities of a damped Timoshenko beam subject to various types of boundary conditions by means of a distributed applied force and moment. An analytic solution is obtained by employing a maximum principle. 相似文献
2.
L.A. Manita 《Journal of Applied Mathematics and Mechanics》2010,74(5):611-616
The problem of minimizing the root mean square deviation of a uniform string with clamped ends from an equilibrium position is investigated. It is assumed that the initial conditions are specified and the ends of the string are clamped. The Fourier method is used, which enables the control problem with a partial differential equation to be reduced to a control problem with a denumerable system of ordinary differential equations. For the optimal control problem in the l2 space obtained, it is proved that the optimal synthesis contains singular trajectories and chattering trajectories. For the initial problem of the optimal control of the vibrations of a string it is also proved that there is a unique solution for which the optimal control has a denumerable number of switchings in a finite time interval. 相似文献
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The initial boundary value problem
$ {*{20}{c}} {\rho {u_{tt}} - {{\left( {\Gamma {u_x}} \right)}_x} + A{u_x} + Bu = 0,} \hfill & {x > 0,\quad 0 < t < T,} \hfill \\ {u\left| {_{t = 0}} \right. = {u_t}\left| {_{t = 0}} \right. = 0,} \hfill & {x \geq 0,} \hfill \\ {u\left| {_{x = 0}} \right. = f,} \hfill & {0 \leq t \leq T,} \hfill \\ $ \begin{array}{*{20}{c}} {\rho {u_{tt}} - {{\left( {\Gamma {u_x}} \right)}_x} + A{u_x} + Bu = 0,} \hfill & {x > 0,\quad 0 < t < T,} \hfill \\ {u\left| {_{t = 0}} \right. = {u_t}\left| {_{t = 0}} \right. = 0,} \hfill & {x \geq 0,} \hfill \\ {u\left| {_{x = 0}} \right. = f,} \hfill & {0 \leq t \leq T,} \hfill \\ \end{array} 相似文献
5.
Philipp Braun Erwin Hernández Dante Kalise 《Bulletin of the Brazilian Mathematical Society》2016,47(1):143-155
We present a computational approach for the construction of reduced-order controllers for the Timoshenko beam model. By means of a space discretization of the Timoshenko equations, we obtain a large-scale, finite-dimensional dynamical system, for which we compute an LQG controller for closed-loop stabilization. The solutions of the algebraic Riccati equations characterizing the LQG controller are then used to construct a balancing transformation which allows the dimensional reduction of the large-scale dynamic compensator. We present numerical tests assessing the stability and performance of the approach. 相似文献
6.
Erwin Hernández Dante Kalise Enrique Otárola 《Journal of Computational and Applied Mathematics》2011,235(5):1383-1393
In this paper we analyze a locking-free numerical scheme for the LQR control of a Timoshenko beam. We consider a non-conforming finite element discretization of the system dynamics and a control law constant in the spatial dimension. To solve the LQR problem we seek a feedback control which depends on the solution of an algebraic Riccati equation. An optimal error estimate for the feedback operator is proved in the framework of the approximation theory for control of infinite dimensional systems. This estimate is valid with constants that do not depend on the thickness of the beam, which leads to the conclusion that the method is locking-free. In order to assess the performance of the method, numerical tests are reported and discussed. 相似文献
7.
Motion planning and boundary control for a rotating Timoshenko beam is presented. Parameterizing the system trajectories by a so‐called flat output, transitions from rest to rest can be achieved in a prescribed finite time. 相似文献
8.
V. K. Bulgakov G. L. Shatov 《Computational Mathematics and Mathematical Physics》2007,47(8):1253-1267
The Pontryagin maximum principle is used to develop an original algorithm for finding an optimal control in a macroeconomic problem. Numerical results are presented for the optimal control and optimal trajectory of the development of a regional economic system. For an optimal control satisfying a certain constraint, an invariant of a macroeconomic system is derived. 相似文献
9.
Nasser-eddine Tatar 《Applicable analysis》2013,92(1):27-43
A viscoelastic Timoshenko beam is investigated. We prove an exponential decay of solutions for a large class of kernels with weaker conditions than the existing ones in the literature. This will allow the use of other types of viscoelastic material for Timoshenko type beams than the usually used ones. 相似文献
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M. Aassila 《Zeitschrift für Angewandte Mathematik und Physik (ZAMP)》2002,15(6):747-768
We study the asymptotic behavior of the system governing the nonlinear vibrations of a Timoshenko beam. 相似文献
12.
Peter Salamon Karl Heinz Hoffmann Anatoly Tsirlin 《Applied Mathematics Letters》2012,25(10):1263-1266
The optimal control for cooling a quantum harmonic oscillator by controlling its frequency is considered. It is shown that this singular problem may be transformed with the proper choice of coordinates to an equivalent problem which is no longer singular. The coordinates used are sufficiently simple that a graphical solution is possible and eliminates the need to use a Weierstrass-like approach to show optimality. The optimal control of this problem is of significance in connection with cooling physical systems to low temperatures. It is also mathematically significant in showing the power and limitations of coordinate transformations for attacking apparently singular problems. 相似文献
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Anca Capatina 《Numerical Functional Analysis & Optimization》2013,34(7-8):817-828
We are interested in finding the coefficient of friction which leads us to a given displacement on the contact surface between an elastic solid body and a rigid foundation. The mathematical formulation of the problem is an optimal control problem governed by a quasivariational inequality. We obtain an approximative caracterization, by using two families of penalized and regularized problems, for a given optimal control. 相似文献
15.
Farid Ammar-Khodja Abdelaziz Soufyane 《Journal of Mathematical Analysis and Applications》2007,327(1):525-538
In this paper we consider a Timoshenko beam with variable physical parameters, we prove that the model can be stabilize by one control force for both internal and boundary cases. 相似文献
16.
We consider a frictionless contact problem with unilateral constraints for a 2D bar. We describe the problem, then we derive its weak formulation, which is in the form of an elliptic variational inequality of the first kind. Next, we establish the existence of a unique weak solution to the problem and prove its continuous dependence with respect to the applied tractions and constraints. We proceed with the study of an associated control problem for which we prove the existence of an optimal pair. Finally, we consider a perturbed optimal control problem for which we prove a convergence result. 相似文献
17.
Samir Adly Maïtine Bergounioux Mohamed Ait Mansour 《Journal of Global Optimization》2010,47(3):421-435
We consider an optimal control where the state-control relation is given by a quasi-variational inequality, namely a generalized obstacle problem. We give an existence result for solutions to such a problem. The main tool is a stability result, based on the Mosco-convergence theory, that gives the weak closeness of the control-to-state operator. We end the paper with some examples. 相似文献
18.
Arezki Touzaline 《应用数学学报(英文版)》2015,31(4):991-1000
19.
研究T im oshenko梁点反馈的稳定性.用线性算子半群方法证明了闭环系统的适定性,并应用算子谱特征得到了闭环系统的强渐近稳定性的充分必要条件.同时,给出了保守系统的几个能观性不等式. 相似文献
20.
Consider the variational inequality for the rectangular dam problem and assume that fluid can be withdrawn from the bottom at a rate proportional tok(x). Denote byp(x, y) the pressure of the fluid in the dam corresponding to a particular choice ofk. Consideringk(x) as a control variable varying in a class {0k(x)N, k(x)dxM}, we introduce the functionalJ(k)=g(y)p(x, y) whereg(y) is a given positive and monotone nondecreasing function. We characterize the controlsk
0 which minimizeJ(k).
This work is partially supported by National Science Foundation MCS-8300293 相似文献
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