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In this paper, we examine the stationary relaxed singular control problem within a multi-dimensional framework for a single agent, as well as its mean field game equivalent. We demonstrate that optimal relaxed controls exist for two problem…
We study a class of zero-sum games between a singular-controller and a stopper over finite-time horizon. The underlying process is a multi-dimensional (locally non-degenerate) controlled stochastic differential equation (SDE) evolving in an…
We establish existence of nearly-optimal controls, conditions for existence of an optimal control and a saddle-point for respectively a control problem and zero-sum differential game associated with payoff functionals of mean-field type,…
The theory of first-order mean field type differential games examines the systems of infinitely many identical agents interacting via some external media under assumption that each agent is controlled by two players. We study the…
We consider a stochastic differential game in the context of forward-backward stochastic differential equations, where one player implements an impulse control while the opponent controls the system continuously. Utilizing the notion of…
Work zone navigation remains one of the most challenging manoeuvres for autonomous vehicles (AVs), where constrained geometries and unpredictable traffic patterns create a high-risk environment. Despite extensive research on AV trajectory…
This paper studies the monotonicity of equilibrium costs and equilibrium loads in nonatomic congestion games, in response to variations of the demands. The main goal is to identify conditions under which a paradoxical non-monotone behavior…
We propose interdependent defense (IDD) games, a computational game-theoretic framework to study aspects of the interdependence of risk and security in multi-agent systems under deliberate external attacks. Our model builds upon…
We consider a zero-sum stochastic differential controller-and-stopper game in which the state process is a controlled diffusion evolving in a multi-dimensional Euclidean space. In this game, the controller affects both the drift and the…
This paper provides necessary and sufficient conditions for a pair of randomised stopping times to form a saddle point of a zero-sum Dynkin game with partial and/or asymmetric information across players. The framework is non-Markovian and…
In this paper, we propose a numerical methodology for finding the closed-loop Nash equilibrium of stochastic delay differential games through deep learning. These games are prevalent in finance and economics where multi-agent interaction…
This paper presents a distributed model predictive control (DMPC) algorithm for a heterogeneous platoon using arbitrary communication topologies, provided each vehicle can communicate with a preceding vehicle in the platoon. The proposed…
An active line of research has considered games played on networks in which payoffs depend on both a player's individual decision and also the decisions of her neighbors. Such games have been used to model issues including the formation of…
Route controlled autonomous vehicles could have a significant impact in reducing congestion in the future. Before applying multi-agent reinforcement learning algorithms to route control, we can model the system using a congestion game to…
Historically, traffic modelling approaches have taken either a particle-like (microscopic) approach, or a gas-like (meso- or macroscopic) approach. Until recently with the introduction of mean-field games to the controls community, there…
Fully autonomous racing demands not only high-speed driving but also fair and courteous maneuvers. In this paper, we propose an autonomous racing framework that learns complex racing behaviors from expert demonstrations using hierarchical…
This paper presents a robust reinforcement learning algorithm called robust deterministic policy gradient (RDPG), which reformulates the H-infinity control problem as a two-player zero-sum dynamic game between a user and an adversary. The…
We propose a hybrid decision-making framework for safe and efficient autonomous driving of selfish vehicles on highways. Specifically, we model the dynamics of each vehicle as a Mixed-Logical-Dynamical system and propose simple driving…
Trajectory planning involving multi-agent interactions has been a long-standing challenge in the field of robotics, primarily burdened by the inherent yet intricate interactions among agents. While game-theoretic methods are widely…
We consider a two player game, where a first player has to install a surveillance system within an admissible region. The second player needs to enter the the monitored area, visit a target region, and then leave the area, while minimizing…