主讲人：倪元华（南开大学） 副教授

主持人：李韬 教授

开始时间：2018-10-18 10:00-11:30

讲座地址：闵行数学楼129报告厅

报告内容摘要：For classical optimal control problem, an optimal control (corresponding to a given time-state initial pair) will stay optimal along the optimal trajectory, namely, the restriction of that optimal control on the tail time horizon will also be optimal for the intertemporal time-state initial pairs. This is termed as the time consistency of optimal control, which is derived by Bellman's principle of optimality. Though not mentioned frequently, time consistency is indeed an essential notion of classical optimal control theory, and Bellman's dynamic programming depends mostly on this time consistency.

In real world, however, the time consistency fails quite often in many situations. The best documented anomalies to ruin Bellman's principle of optimality and the time consistency of optimal control are as follows. The first one is that the discounting function in cost functional is not exponential, and the nonlinear appearance of conditional expectation in cost functional is another factor. The third case is with respect to the state-dependent (or rank-dependent) utility. Such three anomalies can find their strong roots in the areas of economics and finance; and several notable practical examples are the hyperbolic discounting, quasi-geometric discounting, and mean-variance utility.

In this talk, the story about time inconsistency is shed light on including its budding and qualitative analysis since Adam Smith, its quantitative formulation and successful applications in finance and economics, and its growing study in system and control community. Specifically, the necessity is highlighted to study the time inconsistency within the realm of stochastic optimal control.

报告人简介：倪元华，南开大学人工智能学院副教授，2010年毕业于中国科学院数学与系统科学研究院，获理学博士学位。2013.6至2017.1在中国科学院数学与系统科学研究院做博士后，并于2014年5月至2015年5月访问美国加州大学圣地亚哥分校。研究方向为随机控制、最优控制与多个体系统，在SICON, IEEE TAC, Automatica发表长文7篇，并获2016年度关肇直奖。