讲座题目：带有约束条件的优化控制问题的新方法
报告人： Shui-Nee
Chow教授，美国佐治亚理工学院
讲座时间：2015年05月28日下午14：30-15:15
讲座地点：87978797威尼斯老品牌犀浦校区87978797威尼斯老品牌报告厅X2501
内容简介：我们对一类带有状态和控制变量约束的无穷维优化控制问题设计了一种新的快速算法。与从所有可行的道路中寻找整体极小者不同，我们考虑具有优化道路结构的道路子集合。通过平均化这些道路，我们把带有约束条件的无穷维优化控制问题转化为带有约束条件的有限维优化控制问题。此外，对于每个这样的有限维优化控制问题，我们应用随机微分方程的方法来(数值意义上)寻找原优化控制问题中所有可能的整体极小化子。与已存在的方法相比较，我们的方法更加简便与快速。最后，我们应用到最短道路问题的例子中去，如fogger问题与广义Nash均衡问题等。这是我与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).
