Inverse Noncooperative Dynamic Games in Automatic Control

自动控制、经济学和生物学中的许多问题都涉及建模和分析由微分方程控制的动态系统中参与者（或决策者）之间的相互作用。在自动控制领域，非合作微分博弈论因其在鲁棒控制、车辆避碰和驾驶员辅助等问题中的应用而受到广泛关注。此外，最近的实验显示了非合作微分博弈在模拟人机交互或共享控制系统中的描述能力。虽然在开发解决所谓的微分博弈前向问题（即耦合优化问题的解决方案）的概念上花费了大量精力，但通常情况下，逆动态博弈问题只受到很少的关注。在开发逆动态博弈的方法上只花了很少的努力，旨在找到给定测量数据的博弈的成本函数。因此，在上述正向博弈概念的实际应用中，逆动态博弈的解决方案是一个重要的组成部分，因为它们通常需要了解所涉及的成本函数。本项目旨在开发求解逆动态博弈（IDG）的方法。特别是，我们将通过间接方法来解决问题，避免将前向问题的解决作为方法的一部分。这将允许一方面计算上可管理的算法，另一方面，考虑连续值控制和状态空间以及闭环场景。进一步，我们分析了在什么条件下IDG的解是存在的，什么时候这个解是唯一的。手头的提案继续按计划进行第一阶段的成功研究。

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.