【作者】 李雪平；

【导师】 朱位秋；

【作者基本信息】 浙江大学 ， 工程力学， 2008， 博士

【摘要】 本文将导师朱位秋院士提出的“随机激励的耗散的哈密顿系统理论”推广到具有多时滞反馈控制和宽带随机激励下的拟线性系统,研究了多时滞反馈控制和宽带随机激励下的拟线性系统的随机响应,概率为1稳定性,首次穿越时间以及建筑结构在地震作用下的时滞反馈控制的优化。随机响应研究中,将时滞的状态变量在平均意义上用无时滞的状态变量近似,由此得到了无时滞受控的拟可积哈密顿系统,再运用随机平均法,建立相应的Fokker-Planck-Kolmogorov(FPK)方程,求解该方程得到系统的响应,据此研究时滞反馈控制的控制效果;概率为1渐近稳定性研究中,先将时滞系统转化为非时滞系统,再用随机平均法得到关于系统慢变过程的It(?)随机微分方程,再引入新的范数,得到了最大Lyapunov指数的近似表达式,研究系统的概率为1渐近稳定性;首次穿越时间的研究中,先将时滞系统转化为非时滞系统,再用随机平均法得到系统慢变过程的It(?)随机微分方程,然后导出支配条件可靠性函数的后向Kolmotorov方程和支配平均首次穿越时间的Pontrygin方程及边值条件,求解这些方程得到系统的可靠性函数和平均首次穿越时间;在地震作用下建筑结构的时滞反馈控制优化研究中,先假定含待定增益的时滞速度反馈控制,利用随机平均法得到系统概率分布,然后以模态能量和控制力期望最小为性能指标,确定反馈控制增益。以上理论研究的结果和数值模拟结果完全吻合,研究表明时滞对系统的响应、稳定性及首次穿越时间都有不利的影响。但是,如果合理选取时滞时间,这些不利影响几乎可以完全消除。更多还原

【Abstract】 In the present dissertation the theory of stochastically excited and dissipated Hamiltonian systems proposed by W.Q. Zhu is generalized to study the stochastic response, the stochastic stability and the reliability of quasi-linear system under multi-time-delayed feedback control and wide-band random excitations. In the study of the stochastic response, the system equations are transformed into differential equations without time delay and the averaged Ito stochastic differential equations for the slowly varying processes are derived. The stationary solution of the averaged FPK equation associated with the averaged It(o|^) equations is obtained and the effect of time-delayed feedback control on the responses is stuied. In the study of the asymptotic Lyapunov stability with probability 1, the system equations are transformed into differential equations without time delay and the stochastic averaging method is used to derive the averaged Ito differential equations for the slow varing processes. By introducing a new norm, the approximate formula for the largest Lyapunov exponent is derived. The necessary and sufficient condition for the asympototic Lyapunov stability with probability 1 is obtained. In the study of the first-passage failure, the system equations are transformed into differential equations without time delay and the stochastic averaging method is used to derive the averaged Ito differential equations for the slow varing processes. A backward Kolmogorov equation governing the conditional reliability function and a set of generalized Pontryagin equations governing the conditional moments of first-passage time are established. The conditional reliability function and moments of first-passage time are obtained from solving the backward Kolmogorov equation and generalized Pontryagin equations with suitable initial and boundary conditions. In addition, a time-delayed feedback control problem of partially observable linear building structure under horizontal ground acceleration excitation is formulated and converted into that of completely observable linear structure by using the separation principle. The time-delayed control forces are approximately expressed in terms of control forces without time delay. The control system is then governed by Ito stochastic differential equations for the conditional means of system states and then transformed into those for the conditional means of modal energies by using the stochastic averaging method for quasi Hamiltonian systems. The control law is assumed to be modal velocity feedback control with time delay and the unknown control gains are determined by the modal performance indices. The comparising all the theoretic results and those from Monte-Carlo simulation shows that the two results in good agreement. Furthermore, it is shown that the time delay in feedback control affect the response, the asymptotic stability with probability 1 and the first-passage time remarkably. However, the deteriotation effect can be almost eliminated if the delay time is set correctly.更多还原