南开大学机器人与信息自动化研究所 天津市智能机器人技术重点实验室
Institute of Robotics and Automatic Information System Tianjin Key Laboratory of Intelligent Robotics
2016年春季先进机器人与MEMS技术系列学术讲座
Seminar Series：Advanced Robotics & MEMS

报告题目：Optimal control of linear systems with multiplicative noises

时间：2016-05-05 周四 下午2:00-4:00.
地点：信息东楼105教室

个人简介：

苏为洲分别于1983、1986年在东南大学自动控制系获得学士和硕士学位，1996年于新加坡南洋理工大学获得电机工程硕士学位，2000年获澳大利亚纽卡斯大学电机工程博士学位。1986-1994年任教于东南大学自动控制系，2000-2004年在纽卡斯大学、香港科技大学、西悉尼大学等校任博士后研究员。2004年起任教于华南理工大学，现任华南理工大学自动化学院教授、博士生导师。苏为洲教授的研究方向主要包括：网络化控制与估计、鲁棒与最优控制、伺服控制系统。

报告摘要：

This talk presents our recent work in the optimal control design for linear discrete-time systems with stochastic multiplicative uncertainties. These uncertainties are assumed to be present in the control inputs and modeled as independent and identically distributed
random processes. The optimal performance under study is defined in the mean-square sense, referred to as the mean-square optimal H2 performance. It is shown that the mean-square optimal H2 control problem via state feedback can be solved using a mean-square stabilizing solution to a modified algebraic Riccati equation (MARE). A necessary and sufficient condition for the existence of this MARE solution is presented, which constitutes a generalization of the solution to the classic optimal H2 state feedback design problem, whereas the latter can be obtained by solving an algebraic Riccati equation (ARE). It is also proven that the optimal control design problem can be cast as an eigenvalue problem (EVP). With output feedback, we show that the mean-square optimal H2 control problem also amounts to solving an MARE, whenever the plant has no nonminimum phase zeros from the inputs to the measurement outputs, while permitting input delays. Specifically, the global optimal solution is obtained by solving the MARE incorporating the delays. The implication then is that under this circumstance the separation principle still holds in a certain sense.