Time Consistency, Subgame Perfectness, Solution Concepts and Information Patterns in Dynamic Models of Stabilization Policies

Dockner, Engelbert J.; Neck, Reinhard

doi:10.1007/978-3-540-74684-3_4

Cited by 8 publications

(7 citation statements)

References 35 publications

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“…Here, a 'strategy' of a player is a law that tells him/her which action to take at each instant during the game [15]. In other words, it is a mapping from system states or outputs to a player's control action [16]. An equilibrium denotes a strategy profile consisting of the strategies of all the game players in which no one is willing to change his/her strategy unilaterally [17].…”

Section: Introductionmentioning

confidence: 99%

Game-Theoretic Modeling of the Steering Interaction Between a Human Driver and a Vehicle Collision Avoidance Controller

Cole

2015

IEEE Trans. Human-Mach. Syst.

165

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Development of vehicle active steering collision avoidance systems calls for mathematical models capable of predicting a human driver's response so as to reduce the cost involved in field tests whilst accelerate product development. This article provides a discussion on the paradigms that may be used for modelling a driver's steering interaction with vehicle collision avoidance control in path-following scenarios.Four paradigms, namely decentralized, noncooperative Nash, noncooperative Stackelberg and cooperative Pareto are established. The decentralized paradigm, developed based on optimal control theory, represents a driver's interaction with the collision avoidance controllers that disregard driver steering control. The noncooperative Nash and Stackelberg paradigms are used for predicting a driver's steering behaviour in response to the collision avoidance control that actively compensates for driver steering action. These two are devised based on the principles of equilibria in noncooperative game theory. The cooperative Pareto paradigm is derived from cooperative game theory to model a driver's interaction with the collision avoidance systems that take into account the driver's target path. The driver and the collision avoidance controllers' optimization problems and their resulting steering strategies arise in each paradigm are delineated. Two mathematical approaches applicable to these optimization problems, namely the distributed Model Predictive Control and the Linear Quadratic dynamic optimization approaches are described in some detail. A case study illustrating a conflict in steering control between driver and vehicle collision avoidance system is performed via simulation. It was found that variation of driver path-error cost function weights results in a variety of steering behaviours which are distinct between paradigms.

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Section: Introductionmentioning

confidence: 99%

Game-Theoretic Modeling of the Steering Interaction Between a Human Driver and a Vehicle Collision Avoidance Controller

Cole

2015

IEEE Trans. Human-Mach. Syst.

165

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“…p 2 N can be different from the driver's preview horizon p 1 N in theory. Consequently, the environment system equation can be built up by merging target path updating equations (8) and (9) into vehicle dynamics equation (7), which gives:…”

Section: ) Environment Equationmentioning

confidence: 99%

“…A strategy of a game player represents a mapping of the game's states to the player's action [7]. An equilibrium is a strategy set composed of each player's optimal strategy, i.e., the strategy maximizing the player's welfare [8].…”

Section: Introductionmentioning

confidence: 99%

Application of Open-Loop Stackelberg Equilibrium to Modeling a Driver's Interaction with Vehicle Active Steering Control in Obstacle Avoidance

Cole

2017

IEEE Trans. Human-Mach. Syst.

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The increasing use of Active Front Steering (AFS) technology for obstacle avoidance raises the question of drivers' interaction with vehicle automation. Mathematical models capable of representing such interaction are in demand for driver behaviour study. This paper presents the application of open-loop Stackelberg equilibrium to modelling a driver's interaction with vehicle AFS control in an obstacle avoidance scenario, where both the driver and the AFS controller are exerting steering control to the vehicle. In this paper, such driver-AFS interactive steering control is modelled as a leader-follower game. Mathematical expressions of the driver's and the AFS controller's steering control strategies are derived using the Linear Quadratic Dynamic Optimization (LQDO) approach and the Distributed Model Predictive Control (DMPC) approach. These two approaches are found to give identical control gains, which suggests their equivalence in representing driver-AFS interaction. The DMPC approach is found to consume far less computation time due to its numerical nature. Mathematical modifications to the steering control strategies are then introduced to allow practical implementation for a future experimental study. Simulation results including time histories of steering angles and vehicle responses are illustrated and discussed. Index Terms-Driver, Vehicle, Active Front Steering (AFS), Modelling, Game Theory > REPLACE THIS LINE WITH YOUR PAPER IDENTIFICATION NUMBER (DOUBLE-CLICK HERE TO EDIT) <

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“…This class of differential games is the work-horse of the field and has been widely applied in economics. For example, Miller and Salmon [15], Cohen and Michel [7], and Dockner and Neck [8] employ a linear-quadratic differential game to study various macroeconomic issues, Dockner and Long [9] and List and Mason [13] employ the structure to examine various matters in international pollution control, while Groot et al [12] use it to study natural resource extracting firms.…”

Section: A Linear-quadratic Differential Game and Its Olnementioning

confidence: 99%

The Envelope Theorem for Locally Differentiable Nash Equilibria of Discounted and Autonomous Infinite Horizon Differential Games

Ling

Caputo

2012

Dyn Games Appl

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Time Consistency, Subgame Perfectness, Solution Concepts and Information Patterns in Dynamic Models of Stabilization Policies

Cited by 8 publications

References 35 publications

Game-Theoretic Modeling of the Steering Interaction Between a Human Driver and a Vehicle Collision Avoidance Controller

Game-Theoretic Modeling of the Steering Interaction Between a Human Driver and a Vehicle Collision Avoidance Controller

Application of Open-Loop Stackelberg Equilibrium to Modeling a Driver's Interaction with Vehicle Active Steering Control in Obstacle Avoidance

The Envelope Theorem for Locally Differentiable Nash Equilibria of Discounted and Autonomous Infinite Horizon Differential Games

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