一端固定带阻尼项的Timoshenko梁的精确能控性

Exact Controllability of the Damped Timoshenko Beam withone End Fixed

考虑由两个偏微分方程和两个常微分方程控制的一维系统.系统一端固定在刚性天线上,另一端是完全自由的.由于刚性天线连接在系统的一侧,其动力学导致了非标准的边界条件,整个系统成为一个弹性混合系统.利用半群方法研究了系统解的存在唯一性.通过只对系统的一侧施加控制,建立了精确能控性理论.使用希尔伯特唯一性方法,证明了系统在通常能量空间中任意短时间内是精确可控的.

Consider a one‒dimensional system controlled by two partial differential equations and two ordinary differential equations.One end of the system is fixed to a rigid antenna and the other end completely free.Because the rigid antenna is attached to one side of the system,its dynamics result in non‒standard boundary conditions and the whole system becomes an elastic hybrid system.Using semigroup method,the existence and uniqueness of system solutions are studied.By applying control to only one side of the system,we establish the theory of exact controllability.Using the Hilbert uniqueness method,it is proved that the system is exactly controllable in the usual energy space for any short time.We will also estimate the minimum time allowed by the method for the controllability to occur.