Inverse Noncooperative Dynamic Games in Automatic Control

点击翻译按钮获取中文摘要

Numerous problems in automatic control, economics, and biology involve modelling and analyzing interactions between players (or decision makers) in dynamical systems governed by differential equations. In the field of automatic control, noncooperative differential game theory has attracted considerable attention due to its utility in problems such as robust control, vehicle collision avoidance and driver assistance. In addition, recent experiments show the descriptive power of noncooperative differential games in modelling human-machine interaction or shared control systems. While significant effort has been spent at developing concepts of solving the so called forward problem of differential games (i.e. the solution of coupled optimization problems), the inverse dynamic game problem in general has received only scant attention. Only marginal effort has been spent on developing methods for inverse dynamic games, aiming at finding the cost functions of the game given the measurement data. Therefore, the solution of inverse dynamic games represents a significant building block in the real application of the aforementioned forward game concepts, since they often require the knowledge of the involved cost functions. This project aims at developing methods for solving inverse dynamic games (IDG). In particular, we will address the problem by an indirect approach avoiding a solution of the forward problem as part of the method. This will allow on the one hand a computationally manageable algorithm and on the other hand, considering continuous-valued control and state spaces as well as closed loop scenarios. Furthermore, we analyze under which conditions does a solution of the IDG exist and when is this solution unique. The proposal at hand continues the successful research of the first phase as planned.