Inverse Noncooperative Dynamic Games in Automatic Control

自动控制中的逆非合作动态博弈

• 批准号: 421428832
• 负责人: Professor Dr.-Ing. Sören Hohmann
• 金额: --
• 依托单位: Institut für Regelungs- und Steuerungssysteme (IRS)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/421428832?language=en
• 关键词: Inverse; Noncooperative; Dynamic; Games; Automatic

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.

自动控制，经济学和生物学方面的许多问题涉及建模和分析受微分方程管辖的动态系统中玩家（或决策者）之间的相互作用。在自动控制领域，非合作差异游戏理论由于其在诸如强大的控制，避免车辆碰撞和驾驶员帮助之类的问题中引起了极大的关注。此外，最近的实验显示了非合作差异游戏在建模人机相互作用或共享控制系统中的描述能力。尽管已经花费了巨大的努力来开发解决所谓的差分游戏的前瞻性问题（即解决耦合优化问题的解决方案），但总体而言，反向动态游戏问题仅受到了很少的关注。只有边际工作才用于开发用于反向动态游戏的方法，旨在在测量数据的情况下找到游戏的成本功能。因此，反向动态游戏的解决方案代表了上述前向游戏概念的真实应用中的一个重要构件，因为它们通常需要了解涉及的成本功能。该项目旨在开发解决反向动态游戏（IDG）的方法。特别是，我们将通过间接方法来解决问题，以避免解决方案作为方法的一部分。另一方面，考虑到连续值的控制和状态空间以及封闭的循环场景，一方面将允许使用计算可管理的算法。此外，我们分析了存在IDG的解决方案的条件，并且该解决方案何时独特。手头的提案继续按计划进行第一阶段的成功研究。