摘要
在本文中，我们考虑了高维具有强结构阻尼和全指数Ｂａｌａｋｒｉｓｈｎａｎ－Ｔａｙｌｏｒ阻尼的非线性固定边界可伸展的弹性梁方程，得到它的吸收集和平坦惯性流形的存在性．基于无控制方程的惯性流形的存在性，得到了相应的溢出问题的有限维反馈镇定控制．进而，此结果关于结构参数的不确定性是鲁棒的．
A nonlinear hinged extensible elastic body equation with strong structural damping and Balakrishnan-Taylor damping of full exponent is studied as a general model for large space structures of higher dimensions. In this paper, the absorbing sets and flat inertial manifold are obtained for this nonlinear body equation. The control spillover problem associated with the stabilization of this equation is resolved by constructing a linear finite dimensional feedback control based on the existence of inertial manifolds of the uncontrolled equation. Moreover, the results obtained are robust with respect to the uncertainty in structural parameters.
出处
《数学学报（中文版）》
SCIE
CSCD
北大核心
1998年第4期673-678,共6页
Acta Mathematica Sinica：Chinese Series
基金
国家自然科学基金
中物院科学基金
国家攀登计划之一"非线性科学"’资助
