# American Institute of Mathematical Sciences

2013, 3(1): 1-30. doi: 10.3934/naco.2013.3.1

## Jamming in mobile networks: A game-theoretic approach

 1 Department of Mechanical Engineering, Iowa State University, IA, 50011Ames, United States 2 Department of Aerospace Engineering, University of Illinois at Urbana Champaign, IL 61801, Urbana, United States 3 Department of Electrical and Computer Engineering and Coordinated Science Lab, University of Illinois at Urbana Champaign, IL 61801, Urbana, United States

Received  December 2011 Revised  November 2012 Published  January 2013

In this paper, we address the problem of jamming in a communication network within a team of mobile autonomous agents. In contradistinction with the contemporary research regarding jamming, we model the intrusion as a pursuit-evasion game between a mobile jammer and a team of agents.
First, we consider a differential game-theoretic approach to compute optimal strategies for a team of UAVs trying to evade a jamming attack initiated by an aerial jammer in their vicinity. We formulate the problem as a zero-sum pursuit-evasion game, where the cost function is the termination time of the game. We use Isaacs' approach to obtain necessary conditions to arrive at the equations governing the saddle-point strategies of the players. We illustrate the results through simulations. Next, we analyze the problem of jamming from the perspective of maintaining connectivity in a network of mobile agents in the presence of an adversary. This is a variation of the standard connectivity maintenance problem in which the main issue is to deal with the limitations in communications and sensing model of each agent. In our work, the limitations in communication are due to the presence of a jammer in the vicinity of the mobile agents. We compute evasion strategies for the team of vehicles based on the connectivity of the resultant state-dependent graph. We present some simulations to validate the proposed control scheme. Finally, we address the problem of jamming for the scenario in which each agent computes its control strategy based on limited information available about its neighbors in the network. Under this decentralized information structure, we propose two approximation schemes for the agents and study the performance of the entire team for each scheme.
Citation: Sourabh Bhattacharya, Abhishek Gupta, Tamer Başar. Jamming in mobile networks: A game-theoretic approach. Numerical Algebra, Control and Optimization, 2013, 3 (1) : 1-30. doi: 10.3934/naco.2013.3.1
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