精品文档---下载后可任意编辑一类梁振动方程的边界精确零可控性的开题报告题目：一类梁振动方程的边界精确零可控性摘要：本文讨论一类梁振动方程的边界精确零可控性问题，即如何通过在边界施加恰当的控制力，使得系统在有限时间内从任意初始状态达到零状态。我们首先引入梁振动的数学模型，并给出其边界控制问题的定义和解释。接着，我们通过构造 Lyapunov 函数和使用 Laplace 变换等数学工具，得出了该系统边界精确零可控的充分条件。最后，我们给出了模拟和数值计算结果，验证了理论结论的正确性和可行性。关键词：梁振动方程；边界控制；精确零可控性；Lyapunov 函数； Laplace 变换Abstract: This paper studies the exact boundary controllability of a class of beam vibration equations, that is, how to use appropriate control forces on the boundary to make the system reach zero state from any initial state in finite time. We first introduce the mathematical model of beam vibration and give the definition and explanation of its boundary control problem. Then, we obtain the sufficient condition for the exact boundary controllability of the system by constructing Lyapunov function and using Laplace transform and other mathematical tools. Finally, we present simulation and numerical calculation results to verify the correctness and feasibility of the theoretical conclusion.Keywords: beam vibration equation; boundary control; exact controllability; Lyapunov function; Laplace transform.
