Southwest Jiaotong University School of Mathematics


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ag网站亚游登录:   作者:数学中心     日期:2015-05-27 00:00:00   点击数:  


报告人:   Shui-Nee Chow教授,美国佐治亚理工学院



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).

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