Decentralized Opportunistic Navigation Strategies for Multi-agent Systems in the Presence of an Adversary Sourabh Bhattacharya ∗ Abhishek Gupta ∗∗ Tamer Bas ¸ar ∗∗∗ ∗ Coordinated Science Laboratory, University of Illinois at Urbana-Champaign, Urbana, IL 61801, (e-mail: sbhattac@illinois.edu) ∗∗ Aerospace Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, (e-mail: gupta54@illinois.edu) ∗∗∗ Electrical and Computer Engineering, University of Illinois at Urbana-Champaign, Urbana, IL 61801, (e-mail: basar1@illinois.edu) Abstract: We investigate a jamming attack on the communication network of a multi-agent system in a formation. We propose a communication and motion model for the agents. The communication model provides a relation in the spatial domain for effective jamming by an intruder. We formulate the problem as a zero-sum pursuit-evasion game. In our earlier work we used Isaacs’ approach to obtain motion strategies for a network of agents to evade the jamming attack. In this work, we imagine a scenario in which each agent has a knowledge about the value function under perfect state information, beforehand. Due to lack of information about all the agents in the team each agent is constrained to make a local decision based on the information about his neighbors. We propose on-line algorithms under decentralized information patterns which converge for each player. We propose approximation algorithms for the agents, based on averaging and provide some bounds on their performance. 1. INTRODUCTION Electronic warfare has proved to be an efficient combat tech- nique in military scenarios. In the past year, there have been re- ports of predator drones being hacked in Gorman et al. [2009], resulting in intruders gaining access to classified data being transmitted from an aircraft. Unauthorized intrusion of such kind has started a race between the engineers and the hackers as a result of which smarter systems are emerging everyday in order to secure modern instrumentation and software from un- wanted exogenous attacks. This work deals with such a scenario of malicious intrusion and disruption, namely jamming in the communication network of multi-agent systems. Our interest lies in studying the interplay between the communication and the configurational constraints present in mobile multi-agent systems in order to mitigate jamming attacks. Jamming is a malicious attack whose objective is to disrupt the communication of the victim network intentionally, causing interference or collision at the receiver side. Jamming attack is a well-studied and active area of research in wireless networks. Many defense strategies have been proposed by researchers against jamming in wireless networks. A brief survey of various techniques in jamming relevant to our research is provided in Bhattacharya and Bas ¸ar [2010c]. In the case of a single jammer trying to intrude the communication link between a transmitter and a receiver, the problem can be formulated as multiplayer pursuit-evasion game as in Isaacs [1965], Bas ¸ar and Olsder [1999]. In Bhattacharya and Bas ¸ar [2010c], we investigated the problem of finding motion strategies for two UAVs to evade jamming in the presence of an aerial intruder. We considered ⋆ This work was supported in part by an ARO MURI grant and by AFOSR Grant FA9550-09-1-0249. a differential game theoretic approach to compute optimal strategies by a team of UAVs. We formulated the problem as a zero-sum pursuit-evasion game. The cost function was picked as the termination time of the game. We used Isaacs’ approach to derive the necessary conditions to arrive at the equations governing the saddle-point strategies of the players. In Bhattacharya and Bas ¸ar [2010d], we extended the previous analysis to a team of heterogeneous vehicles containing UAVs and autonomous ground vehicles (AGVs). In the case when we have three or more agents in the network, we can pose the problem of mitigating the adverse effects of jamming as a connectivity maintenance problem in multi-agent systems. Substantial research has been done in the recent past to address the problem of maintaining connectivity in mobile networks; for example, Ji and Egerstedt [2006], DeGennaro and Jadbabaie [2006], Notarstefano et al. [2006], Zavlanos and Pappas [2008], Zavlanos and Pappas [2007]. In Bhattacharya and Bas ¸ar [2010b], we had addressed the problem of a team of mobile agents that try to maintain connectivity in the commu- nication network in the presence of a jammer in the vicinity. This analysis was based on the assumption that each agent had a perfect state information about all the other agents. In reality, the presence of a jammer in the vicinity renders the commu- nication network to be a sparsely connected graph. This leads to congestion and eventually an overall delay in exchanging state information among all the agents in the team. Therefore, the solution to the original game under full-state perfect in- formation pattern is rendered inutile. In the past, derivation of distributed algorithms for the computation of non-cooperative equilibria of certain classes of games has been addressed in Bas ¸ar and Li [1989], Li and Basar [1987]. It has been shown in these papers that when the cost function is convex or if the Preprints of the 18th IFAC World Congress Milano (Italy) August 28 - September 2, 2011 Copyright by the International Federation of Automatic Control (IFAC) 11809