一类时滞非线性系统随机动力学与控制

项目名称： 一类时滞非线性系统随机动力学与控制

项目编号： No.11202061

项目类型： 青年科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 冯长水

作者单位： 杭州电子科技大学

项目金额： 24万元

中文摘要： 本项目主要研究一类时滞非线性系统随机动力学与控制，初步建立起一套含时滞反馈的非线性振动系统随机动力学与控制的理论和方法。根据系统的可积性与共振性，假设系统当前状态与过去状态满足广义谐和函数关系，发展适合于含时滞反馈的多自由度非线性随机动力学系统的随机平均法，利用扩散过程理论研究系统的随机响应、首次穿越、随机稳定性及随机分岔等动力学特性；并结合Bellman动态规划原理，分别以响应最小化、可靠度最大化或稳定度最大化为目标，发展一套计及状态部分观测、控制力有界等因素的时滞随机最优控制理论方法；进而，研究时滞随机最优控制系统的动力学，包括响应、可靠性、稳定性、分岔等，通过与未控系统动力学的比较，建立控制性能指标与受控系统动力学变化之间的关系，以便更有目的更有效的控制系统。最后，用Monte Carlo数字模拟法验证上述理论方法的有效性。

中文关键词： 非线性系统；时滞；随机动力学；随机控制；随机平均法

英文摘要： The project is mainly to study the stochastic dynamics and control of a class of nonlinear systems with time delays. A set of theory to study the stochastic dynamics and control of nonlinear vibration systems with time delays will be proposed and develped. Based on integrability and resonance of the systems, assuming that the relationship between the past state and the current state can be expressed as the generalized harmonic functions, the stochastic averaging method for multi-degree of freedom nonlinear stochastic dynamical systems with time delays will be developed. The stochastic response, first-passage time, stochastic stability and stochastic bifurcation of the systems will be studied by using diffusion process method. A class of time-delay stochastic optimal control strategies for partially observable nonlinear systems with actuator saturation will be proposed and developed based on the stochastic averaging method and the dynamical programming principle. The control strategies will be applied to the systems for minimizing the response, maximizing the reliability or mean first-passage time and stabilization. Furthermore, the dynamics properties of controlled systems will be studied, by camparison with those of the uncontrolled systems, the relationship between performance index and the dynamics propreties

英文关键词： Nonlinear system；Time delay；Stochastic dynamics；Stochastic control；Stochastic averaging method