Solution Sets for Inverse Non-Cooperative Linear-Quadratic Differential Games

This letter addresses the inverse problem of differential games, where the aim is to compute cost functions which lead to observed Nash equilibrium trajectories. The solution of this problem allows the generation of a model for inferring the intent of several agents interacting with each other. We present a method to find all cost functions which lead to the same Nash equilibrium in an infinite-horizon LQ differential game. The approach relies on a reformulation of the coupled matrix Riccati equations which arise out of necessary and sufficient conditions for Nash equilibria. Furthermore, based on our findings, we present an approach to compute a solution given a set of observed state and control trajectories. Our results highlight properties of feedback Nash equilibria in LQ differential games and provide an efficient approach for the estimation of cost function matrices in such a scenario

Inverse Open-Loop Noncooperative Differential Games and Inverse Optimal Control

We consider the problem of computing parameters of player cost functionals such that given state and control trajectories constitute an open-loop Nash equilibrium for a noncooperative differential game. We propose two methods for solving this inverse differential game problem and novel conditions under which our methods compute unique cost-functional parameters. Our conditions are analogous to persistence of excitation conditions in adaptive control and parameter estimation. The efficacy of our methods is illustrated in simulations

Modelling of a Human Driver’s Interaction with Vehicle Automated Steering using Cooperative Game Theory

The introduction of automated driving systems raised questions about how the human driver interacts with the automated system. Non-cooperative game theory is increasingly used for modelling and understanding such interaction, while its counterpart, cooperative game theory is rarely discussed for similar applications despite it may be potentially more suitable. This paper describes the modelling of a human driver’s steering interaction with an automated steering system using cooperative game theory. The distributed Model Predictive Control approach is adopted to derive the driver’s and the automated steering system’s strategies in a Pareto equilibrium sense, namely their cooperative Pareto steering strategies. Two separate numerical studies are carried out to study the influence of strategy parameters, and the influence of strategy types on the driver’s and the automated system’s steering performance. It is found that when a driver interacts with an automated steering system using a cooperative Pareto steering strategy, the driver can improve his/her performance in following a target path through increasing his/her effort in pursuing his/her own interest under the driver-automation cooperative control goal. It is also found that a driver’s adoption of cooperative Pareto steering strategy leads to a reinforcement in the driver’s steering angle control, compared to the driver’s adoption of non-cooperative Nash strategy. This in turn enables the vehicle to return from a lane-change maneuver to straight-line driving swifter

Kooperative Regelungskonzepte auf Basis der Spieltheorie und deren Anwendung auf Fahrerassistenzsysteme

Cooperative control loops in which human and a technical automation system perform a control task in close cooperation are investigated. A control framework is proposed which is based on a formal description of the cooperative control problem. The main idea of the control algorithm is to solve a differential game on a sliding horizon. The concept has been applied to design two cooperative advanced driver-assistance systems. One for the longitudinal driving task, one for the lateral driving task

Kooperative Regelungskonzepte auf Basis der Spieltheorie und deren Anwendung auf Fahrerassistenzsysteme

Diese Arbeit betrachtet Regelkreise, in denen die Regelaufgabe von Menschen und maschinellen Reglern gemeinsam ausgeführt wird. Für diese maschinellen Regler wird systematisch ein formalisiertes Regelkonzept abgeleitet. Ein wesentlicher Teil der Arbeit besteht in der Entwicklung von Algorithmen für die Implementierung. Als Anwendungsbeispiel werden zwei kooperative Fahrerassistenzsysteme vorgestellt. Am Fahrsimulator durchgeführte Studien zeigen eine deutliche Verbesserung des Fahrverhaltens aber auch des Kraftstoffverbrauchs