講座題目：帶有約束條件的優(yōu)化控制問題的新方法

報(bào)告人：   Shui-Nee Chow教授，美國(guó)佐治亞理工學(xué)院

講座時(shí)間：2015年05月28日下午14：30-15:15

講座地點(diǎn)：kaiyun開云官方網(wǎng)站犀浦校區(qū)kaiyun開云官方網(wǎng)站報(bào)告廳X2501

內(nèi)容簡(jiǎn)介：我們對(duì)一類帶有狀態(tài)和控制變量約束的無窮維優(yōu)化控制問題設(shè)計(jì)了一種新的快速算法。與從所有可行的道路中尋找整體極小者不同，我們考慮具有優(yōu)化道路結(jié)構(gòu)的道路子集合。通過平均化這些道路，我們把帶有約束條件的無窮維優(yōu)化控制問題轉(zhuǎn)化為帶有約束條件的有限維優(yōu)化控制問題。此外，對(duì)于每個(gè)這樣的有限維優(yōu)化控制問題，我們應(yīng)用隨機(jī)微分方程的方法來(數(shù)值意義上)尋找原優(yōu)化控制問題中所有可能的整體極小化子。與已存在的方法相比較，我們的方法更加簡(jiǎn)便與快速。最后，我們應(yīng)用到最短道路問題的例子中去，如fogger問題與廣義Nash均衡問題等。這是我與Magnus Egerstedt (ECE, Georgia Tech). Wuchen Li (Georgia Tech), Jun Lu (Wells Fargo) 和Haomin Zhou (Georgia Tech)一起合作的工作。

Title: A New Approach to Optimal Control with Constraints

Reporter: Professor Shui-Nee Chow, Georgia Institute of Technology

Abstract: We design a new fast algorithm for a class of infinite dimensional optimal control problems with constraints on both state and control variables. Instead of searching global minimizer(s) from all feasible paths, we consider  the subset of paths with structure of optimal paths. By leveraging these paths, we transfer our infinite dimensional optimal control problem with constraints to a set of finite and different dimensional optimization problems with constrains. Moreover, for each of these finite dimensional optimal control problems, we apply methods from stochastic differential equations in order to find numerically all possible global minimizers of our original optimal control problem. Comparing to the existing methods, our method is fundamentally easier and faster. Examples for some shortest path problems, fogger problem and generalized Nash equilibrium will be presented. This is joint work with Magnus Egerstedt (ECE, Georgia Tech). Wuchen Li (Georgia Tech), Jun Lu (Wells Fargo) and Haomin Zhou (Georgia Tech).