Resilient and decentralized control of multi-level cooperative mobile networks to maintain connectivity under adversarial environment

Network connectivity plays an important role in the information exchange between different agents in the multi-level networks. In this paper, we establish a game-theoretic framework to capture the uncoordinated nature of the decision-making at different layers of the multi-level networks. Specifically, we design a decentralized algorithm that aims to maximize the algebraic connectivity of the global network iteratively. In addition, we show that the designed algorithm converges to a Nash equilibrium asymptotically and yields an equilibrium network. To study the network resiliency, we introduce three adversarial attack models and characterize their worst-case impacts on the network performance. Case studies based on a two-layer mobile robotic network are used to corroborate the effectiveness and resiliency of the proposed algorithm and show the interdependency between different layers of the network during the recovery processes.

[1]  Gordon F. Royle,et al.  Algebraic Graph Theory , 2001, Graduate texts in mathematics.

[2]  Bernhard Ganter,et al.  Formal Concept Analysis: Mathematical Foundations , 1998 .

[3]  Antonio Scala,et al.  Networks of Networks: The Last Frontier of Complexity , 2014 .

[4]  Ugur Zengin,et al.  Real-Time Target Tracking for Autonomous UAVs in Adversarial Environments: A Gradient Search Algorithm , 2007, IEEE Transactions on Robotics.

[5]  J. Lofberg,et al.  YALMIP : a toolbox for modeling and optimization in MATLAB , 2004, 2004 IEEE International Conference on Robotics and Automation (IEEE Cat. No.04CH37508).

[6]  Walid Saad,et al.  Eavesdropping and jamming in next-generation wireless networks: A game-theoretic approach , 2011, 2011 - MILCOM 2011 Military Communications Conference.

[7]  M. Fiedler.  Algebraic connectivity of graphs , 1973 .

[8]  J.A. Stankovic,et al.  Denial of Service in Sensor Networks , 2002, Computer.

[9]  Charles R. Johnson,et al.  Matrix analysis , 1985, Statistical Inference for Engineers and Data Scientists.

[10]  Siddhartha S. Srinivasa,et al.  Decentralized estimation and control of graph connectivity in mobile sensor networks , 2008, 2008 American Control Conference.

[11]  C. Karlof,et al.  Secure routing in wireless sensor networks: attacks and countermeasures , 2003, Proceedings of the First IEEE International Workshop on Sensor Network Protocols and Applications, 2003..

[12]  Li-Der Chou,et al.  A survey of black hole attacks in wireless mobile ad hoc networks , 2011, Human-centric Computing and Information Sciences.

[13]  Harsha Nagarajan,et al.  Algorithms for synthesizing mechanical systems with maximal natural frequencies , 2012 .

[14]  Lorenzo Sabattini,et al.  Decentralized connectivity maintenance for cooperative control of mobile robotic systems , 2013, Int. J. Robotics Res..

[15]  L. Shapley,et al.  Potential Games , 1994 .

[16]  Dennis M. Akos,et al.  Who's Afraid of the Spoofer? GPS/GNSS Spoofing Detection via Automatic Gain Control (AGC) , 2012 .

[17]  Robert H. Deng,et al.  Detecting node replication attacks in mobile sensor networks: theory and approaches , 2012, Secur. Commun. Networks.

[18]  Quanyan Zhu,et al.  Interdependent network formation games with an application to critical infrastructures , 2016, 2016 American Control Conference (ACC).

[19]  Wenyuan Xu,et al.  Jamming sensor networks: attack and defense strategies , 2006, IEEE Network.

[20]  Jon C. Dattorro,et al.  Convex Optimization & Euclidean Distance Geometry , 2004 .

[21]  Rutvij H. Jhaveri,et al.  DoS Attacks in Mobile Ad Hoc Networks: A Survey , 2012, 2012 Second International Conference on Advanced Computing & Communication Technologies.

[22]  Ran Dai,et al.  Optimal topology design for dynamic networks , 2011, IEEE Conference on Decision and Control and European Control Conference.

[23]  George J. Pappas,et al.  Distributed connectivity control of mobile networks , 2007, 2007 46th IEEE Conference on Decision and Control.

[24]  Mehran Mesbahi,et al.  On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian , 2006, IEEE Transactions on Automatic Control.

[25]  Huijuan Wang,et al.  Algebraic Connectivity of Interdependent Networks , 2014 .

[26]  Nei Kato,et al.  A survey of routing attacks in mobile ad hoc networks , 2007, IEEE Wireless Communications.

[27]  David Tse,et al.  Fundamentals of Wireless Communication , 2005 .

[28]  Satria Mandala,et al.  A Review of Current Routing Attacks in Mobile Ad Hoc Networks , 2008 .

[29]  Todd E. Humphreys,et al.  Unmanned Aircraft Capture and Control Via GPS Spoofing , 2014, J. Field Robotics.

[30]  Stephen P. Boyd,et al.  Growing Well-connected Graphs , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[31]  M. Mesbahi,et al.  On maximizing the second smallest eigenvalue of a state-dependent graph Laplacian , 2005, Proceedings of the 2005, American Control Conference, 2005..

[32]  Vijay Kumar,et al.  Maintaining Connectivity in Mobile Robot Networks , 2008, ISER.

[33]  Ugur Zengin,et al.  Real-Time Target Tracking for Autonomous UAVs in Adversarial Environments: A Gradient Search Algorithm , 2006, Proceedings of the 45th IEEE Conference on Decision and Control.

[34]  Robert Babuška,et al.  On distributed maximization of algebraic connectivity in robotic networks , 2011, Proceedings of the 2011 American Control Conference.