最优有界控制下色噪声驱动多时滞拟线性系统瞬态响应  

The transient response of the multi-delayed quasi-linear system with colored noise excitations and optimal bounded control

作　　者：戚鲁媛[1] 徐伟[1] 高维廷[2] 

机构地区：[1]西北工业大学理学院,陕西西安710129 [2]西北工业大学电子信息学院,陕西西安710129

出　　处：《振动工程学报》2013年第6期846-853,共8页Journal of Vibration Engineering

基　　金：国家自然科学基金(11172233;10932009;61171155);陕西省自然科学基金(2012JM8010);西北工业大学博士论文创新基金资助项目(CX201215)

摘　　要：基于Fokker-Planck-Kolmogorov方程瞬态求解研究了受最优有界控制的色噪声驱动的多时滞拟线性系统的瞬态响应。利用等价变换将时滞系统转化为非时滞系统。在弱扰动假设下应用标准随机平均法得到振幅过程的部分平均It随机微分方程。由动态规划原理和控制力界值条件得到最优有界控制率,从而得到完全平均的Fokker-Planck-Kolmogorov方程。通过原系统的退化线性系统导出一组正交基并在该基空间内进行Galerkin变分得到近似瞬态响应。最后将该方法应用到受最优有界控制率和色噪声共同作用的时滞Duffing-Van Der Pol振子进行理论求解,并综合讨论了色噪声、时滞、控制力和共振对系统瞬态响应的影响,采用Monte-Carlo模拟验证了所有理论和计算结果的正确性。The transient responses of an optimally controlled multi-delayed quasi-linear system driven by colored noise excita- tions are studied through Fokker-Planck-Kolmogorov equation. The time-delayed system is firstly transformed to an equivalent delay-freee system. The standard stochastic averaging method is then applied to obtain the partially averaged It？ stochastic dif- ferential equation for the amplitude process of the original system. Afterwards, based on the dynamical programming principle and the bounded value condition of control, the dynamical programming equation is built and the optimal bounded control algo- rithm for minimizing the system response is obtained, thereby leading to the complete averaged FPK equation for the amplitude process. A set of orthogonal basis functions are obtained by applying the eigenfunction method to the degenerated linear FPK e- quation. The approximate probability densities are obtained by applying the Galerkin method to the complete averaged FPK e- quation in the orthogonal basis space. Finally, the analysis procedure is applied to study a time-delayed Duffing-Van Der Pol oscillator with optimal bounded control and a colored noise excitation, wherein the effects of the colored noise, the time delay, the control force and the resonance on the nonstationary response of system are discussed. All the results are verified through conducting Monte Carlo Simulation.

关 键 词：随机振动 GALERKIN法 瞬态概率密度 时滞 最优有界控制 

分 类 号：O324[理学—一般力学与力学基础] O322[理学—力学]