A differential game with two pursuers and one evader

2011

Auton Robot

In this paper, we address the problem of a mobile intruder jamming the communication network in a vehicular formation. In order to understand the spatial aspect of the jamming problem, we consider a jamming model that takes into account the relative distance of the jammer from the vehicles. We formulate the problem as a zero-sum pursuitevasion game between a jammer and a team of players with players possessing heterogeneous dynamics. We use Isaacs' approach to arrive at the equations governing the optimal strategies of the team of players. Finally, we obtain the optimal trajectories in the neighborhood of termination by numerically simulating the strategies for some variants of the problem.

Section: Introductionmentioning

confidence: 97%

Spatial approaches to broadband jamming in heterogeneous mobile networks: a game-theoretic approach

2011

Auton Robot

Section: Introductionmentioning

confidence: 99%

Multi-layer hierarchical approach to double sided jamming games among teams of mobile agents

2012 IEEE 51st IEEE Conference on Decision and Control (CDC)

2012

Abstract-In this paper, we study the trade off in resource allocation between malicious intrusion (jamming) and communication/coordination by two teams of mobile agents. Agents belonging to the same team communicate over wireless ad hoc networks, and they distribute their available power between the tasks of communication and jamming the communication network nodes of the other team. This is a generalization of our earlier work in [7] which considered the special case when each team consists of only two agents. Here we consider the nontrivial extension to multiple agents (in each team). The agents have constraints on their total energy and instantaneous power usage. The cost function adopted is the difference between the rates of erroneously transmitted bits of each team.We model the problem as a zero-sum differential game between the two teams (where the teams are the actual players in the zero-sum game) and use Isaacs' approach to obtain necessary conditions for the corresponding trajectories. The solution to the optimal control problem for each team in turn depends on the solution to the power allocation problem for each agent. The power allocation problem is a non-zero sum game between the two teams, and we present sufficient conditions for the existence of a pure strategy Nash equilibrium. Finally, we provide some simulation results to validate the approach taken.

“…Recent efforts in this direction to compute an approximation of the reachable sets have been provided by Mitchell and Tomlin [17], Stipanović, Hwang and Tomlin [22], and Stipanović, Sriram and Tomlin [24]. Solutions for particular multi-player games were presented by Pashkov and Terekhov [19], Levchenkov and Pashkov [12], Hagedorn and Breakwell [9], Breakwell and Hagedorn [7], Sriram et al [21], and recently, by Fuchs et al [8]. More general treatments of multiplayer differential games were presented by Starr and Ho [6], Vaisbord and Zhukovskiy [26], Zhukovskiy and Salukvadze [27], and Stipanović, Hovakimyan and Melikyan [23].…”

Section: Introductionmentioning

confidence: 99%

Singular surfaces in multi-agent connectivity maintenance games

IEEE Conference on Decision and Control and European Control Conference

Hovakimyan

2011

Abstract-In this paper, we analyze a connectivity maintenance problem that arises when two mobile autonomous agents navigate in an environment containing obstacles. Using the Rician fading model for the communication channel, we address the problem for the case when the motion strategies for one of the agents is adversarial in nature. We investigate a specific kind of singular surface that appears in the solution to the underlying pursuit-evasion game, namely the dispersal surface. We present construction of the projection of several dispersal surfaces for various obstacle geometries by fixing the initial position of the evader. Finally, we present numerical simulations for specific environments containing obstacles.