非线性随机动力学和控制研究进展及展望.pdfVIP

2005 2 世界科技研究与发展 非线性随机动力学与 控制研究进展及展望 ( , 310027) : 随机动力学系用概率与统计方法研究自然界工程及社会中各种随机动力学过程与现象 经 个世纪的发展, 非线性随机动力学与控制已有相当的理论方法, 主要是扩散过程理论方法本 文概述该理论方法, 特别是作者提出与发展的非线性随机动力学与控制的Hamilt on 理论体系框 架最后建议各领域随机动力学与控制研究者进行跨学科的合作研究 : 随机动力学 随机稳定性 随机分岔 首次穿越 随机控制 非线性系统 Recent Developments in Nonlinear Stochastic Dynamics and Control Member of The CAS ZHU Weiqi (Department of Mechanics, Zhejiang University, Hangzho 310027) Abstract:Stochastic dynamics studies various stochastic dynamical p rocesses and p henomena in na- ture, engineering and society using p robability and statistics. Af ter the develop ments in the last cen- tury , nonlinear stochastic dynamics has p lenty of theories and methods, among which the theory and method of diff usionp rocesses are dominant. Thep resent p ap er outlines this theory and method, es- p ecially theHamiltonian theoreticalf ramework of nonlinear stochastic dynamics and controlp roposed and develop ed by thep resent author. Finally, the collaboration of researchers in variousf ields of stochastic dynamics and control is suggested. Key words: stochastic dynamics, stochastic stability, stochastic bif urcation, f irst-passage time, stochastic control, nonlinear system , 10 , 20 Einst ein , 1940s 1960s , , , 1980s , , 1960s, www . globesci. com Vol . 27 N o. 1 1 世界科技研究与发展 2005 2 , , , , 60 1980s , , 1970s