基于状态空间离散的高维不确定非线性系统振动与控制分析方法

项目名称： 基于状态空间离散的高维不确定非线性系统振动与控制分析方法

项目编号： No.11332008

项目类型： 重点项目

立项/批准年度： 2014

项目学科： 数理科学和化学

项目作者： 江俊

作者单位： 西安交通大学

项目金额： 300万元

中文摘要： 现代工程装备中的不确定性和非线性因素对装备性能的优化和可靠性的提升所产生的影响日益突出，高维不确定非线性系统的振动与控制分析理论和方法已成为有着工程需求的重要学科前沿性课题。本项目拟基于状态空间离散的思路，通过研究高维随机和模糊不确定非线性系统的短时解析解，以建立起高维不确定非线性系统的稳态与瞬态响应及其分布的高效的半解析数值方法；并在此方法框架的基础上，结合系统不确定性与非线性全局结构相互作用的机制和不确定性扰动效果的定量分析的研究，发展一套面向工程实际的高维随机和模糊不确定非线性系统安全域及内部响应分布的定量预估方法；通过发展高维动态规划方程的高效求解方法，构建满足工程需求的非线性随机最优控制的设计方法；最后开展具有工程背景的不确定多自由度非线性系统的实验研究，以验证所提出的理论和方法。本项目属于非线性科学与工程学科交叉性的应用基础前沿研究,对动力学和控制学科的发展有重要意义。

中文关键词： 高维非线性系统;随机与模糊不确定性;振动与控制;状态空间离散化;半解析数值方法

英文摘要： Uncertainties and nonlinearities in engineering equipment play an increasingly important role in the optimization of system performance and reliability. Consequently, development of effective methods for analysis and control of system vibration of high-dimensional engineering systems has become an urgent subject of advanced scientific research. This project presents a program to develop such a method based on the concept of discretizing the state space. In particular, the method makes use of analytical solutions of short-time solutions to formulate the generalized cell mapping of high-dimensional uncertain stochastic or fuzzy nonlinear systems resulting in a semi-analytical numerical approach for obtaining transient and steady-state response and its distribution. This semi-analytical method is then applied to quantitatively investigate the interactions between uncertainties and nonlinear global response topology, to develop a practical method for predicting the response distribution of high-dimensional stochastic or fuzzy nonlinear systems in a safety domain. The method is also applied to obtain solutions of dynamic programming for nonlinear stochastic optimal controls to meet the needs of engineering applications. Finally, experimental validation of the theory and method will be conducted by developing the test rigs of engineering relevance. This project represents state-of-the art interdisciplinary research of nonlinear science and engineering, will advance the discipline of dynamics and control and has broad impact to engineering disciplines.

英文关键词： high-dimensional systems;stochastic/fuzzy uncertainty;vibration and control;state space discretization;semi-analytical methods