A Numerical Method of Local Energy Decay for the Boundary Controllability of Time‐Reversible Distributed Parameter Systems
A Numerical Method of Local Energy Decay for the Boundary Controllability of Time‐Reversible Distributed Parameter Systems
复制标题
时间可逆分布参数系统边界可控性的局域能量衰减数值方法
DOI：
10.1111/j.1467-9590.2008.00406.x
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发表时间：
2008
影响因子：
2.7
通讯作者：
J. Villena
中科院分区：
文献类型：
--
作者：
P. Pedregal;F. Periago;J. Villena
本文研究线性、时间可逆、二阶演化系统的边界控制的数值计算。基于 Russell (Stud. Appl. Math. LII(3) (1973)) 引入的波动方程方法，提出了解决此类问题的数值算法。该方法的收敛基于与原始控制系统相关的适当柯西问题的解的局部能量衰减。该方法通过对一维克莱因-戈登和欧拉-伯努利方程、矩形上的波动方程和圆盘上的板方程的多次数值模拟进行了说明。
This paper deals with the numerical computation of the boundary controls of linear, time‐reversible, second‐order evolution systems. Based on a method introduced by Russell (Stud. Appl. Math. LII(3) (1973)) for the wave equation, a numerical algorithm is proposed for solving this type of problems. The convergence of the method is based on the local energy decay of the solution of a suitable Cauchy problem associated with the original control system. The method is illustrated with several numerical simulations for the Klein–Gordon and the Euler–Bernoulli equations in 1D, the wave equation on a rectangle, and the plate equation on a disk.