拟哈密顿系统非线性随机最优控制

朱位秋; 应祖光

doi:10.6052/1000-0992-12-045

拟哈密顿系统非线性随机最优控制

doi: 10.6052/1000-0992-12-045

浙江大学航空航天学院力学系, 杭州310027

基金项目: 国家自然科学基金重点项目(10932009)和面上项目(11072212,11072215,11272279)资助

详细信息

作者简介:
朱位秋, 男, 汉族, 浙江义乌人. 现为浙江大学航空航天学院应用力学研究所教授, 博士生导师, 所长, 中国科学院院士. 1967s1975 年在飞机结构强度研究所工作, 1975 年调浙江大学任教. 曾先后访问美国Wisconsin Univ., MIT, Florida Atlantic Univ., New York State Univ. at Buffalo, 日本Kyoto Univ.等. 长期从事非线性随机动力学与控制研究, 他领导课题组创建了非线性随机动力学与控制的哈密顿理论体系, 2002 年获国家自然科学二等奖.

通讯作者:
朱位秋

中图分类号: O32,O23,TB123
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出版历程
- 收稿日期: 2012-03-26
- 修回日期: 2012-11-14
- 刊出日期: 2013-01-24

ADVANCES IN RESEARCH ON NONLINEAR STOCHASTIC OPTIMAL CONTROL OF QUASI-HAMILTONIAN SYSTEMS

Department of Mechanics, School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China

Funds: The project was supported by the National Natural Science Foundation of China (10932009, 11072212, 11072215, 11272279).

More Information

Corresponding author: ZHU Weiqiu

摘要

摘要: 主要介绍近十几年来拟哈密顿系统非线性随机最优控制理论方法及其应用的研究成果, 包括基于拟哈密顿系统随机平均法与随机动态规划原理的非线性随机最优控制基本策略, 即响应极小化控制、随机稳定化、首次穿越损坏最小化控制、以概率密度为目标的控制, 为将它们应用于工程实际而作的部分可观测系统最优控制、有界控制、时滞控制、半主动控制、极小极大控制的进一步研究, 以及综合考虑这些实际问题的非线性随机最优控制的综合策略, 非线性随机最优控制在滞迟系统、分数维系统等中的若干应用, 介绍与这些研究有关的背景, 并指出今后有待进一步研究的问题.
- 拟哈密顿系统 /
- 非线性随机动力学 /
- 非线性随机最优控制 /
- 随机平均 /
- 随机动态规划
Abstract: Advances in the theory of nonlinear stochastic optimal control of quasi-Hamiltonian systems and its applications in the last decade is summarized. It includes: (1) the basic nonlinear stochastic optimal control strategies based on the stochastic averaging method for quasi-Hamiltonian systems and the stochastic dynamical programming principle, that is, response minimization control, stochastic stabilization, first-passage failure minimization control, and the control for targeting a specified stationary probability density function; (2) further study on the nonlinear stochastic optimal control for application, such as optimal control of partially observable systems, bounded optimal control, time-delay optimal control, semi-active optimal control and minimax control; (3) the integrated nonlinear stochastic optimal control strategy; (4) the applications of the nonlinear stochastic optimal control strategy to engineering structures including hysteretic systems and fractional derivative systems. Some related background and problems to be studied in future are also pointed out.
- quasi-Hamiltonian system /
- nonlinear stochastic dynamics /
- nonlinear stochastic optimal control /
- stochastic averaging /
- stochastic dynamical programming

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