中文摘要：

无常在几乎所有设计系统固有、不可避免。借助于可靠性途径处理无常并且在不明确的系统的控制设计对无常和系统性能完成在可靠性之间的合理平衡具有必要意义。不过，能面对无常为结构的活跃控制的分析和合成直接被使用的可靠性方法尚待被发展，特别处于非概率的无常状况。在现在的纸，不明确的结构使用的颤动控制的问题线性二次的管理者(LQR ) 途径从可靠性的观点被学习。不明确的结构的柔韧的控制被对待介绍的为基于 LQR 的静态的输出反馈的一个有效非概率的柔韧的可靠性方法作为间隔变量围住不明确的参数。为不明确的结构的最佳的颤动控制器设计被与目的解决一个柔韧的基于可靠性的优化问题最小化二次的表演索引执行。获得的控制器可以在控制结构关于可被考虑的无常是要用体力地可靠的条件下面拥有最佳性能。建议方法为在不明确的结构的控制器设计完成在坚韧性和性能之间的平衡提供一个必要基础。介绍明确的表达在线性矩阵不平等的框架并且能方便地被执行。二个数字例子被提供说明现在的方法的有效性和可行性。

英文摘要：

Uncertainty is inherent and unavoidable in almost all engineering systems. It is of essential significance to deal with uncertainties by means of reliability approach and to achieve a reasonable balance between reliability against uncertainties and system performance in the control design of uncertain systems. Nevertheless, reliability methods which can be used directly for analysis and synthesis of active control of structures in the presence of uncertainties remain to be developed, especially in non-probabilistic uncertainty situations. In the present paper, the issue of vibration con- trol of uncertain structures using linear quadratic regulator （LQR） approach is studied from the viewpoint of reliabil- ity. An efficient non-probabilistic robust reliability method for LQR-based static output feedback robust control of un- certain structures is presented by treating bounded uncertain parameters as interval variables. The optimal vibration con- troller design for uncertain structures is carried out by solv- ing a robust reliability-based optimization problem with the objective to minimize the quadratic performance index. The controller obtained may possess optimum performance un- der the condition that the controlled structure is robustly re- liable with respect to admissible uncertainties. The proposed method provides an essential basis for achieving a balance between robustness and performance in controller design ot uncertain structures. The presented formulations are in the framework of linear matrix inequality and can be carried out conveniently. Two numerical examples are provided to illustrate the effectiveness and feasibility of the present method.