拟哈密顿系统非线性随机最优控制

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.

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

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.