Consequences of topological changes in cyber-physical networks A system-theoretic perspective

In this chapter we study an example of a change in actuational topology of a Linear Networked Synchronization Process. We motivate the problem as a study of vulnerability of a LNSP to intrusion by an external adversary that has gained actuational capabilities at a single (or a few) network component. Specifically, we model the intruder as seeking to move the state of the synchronization process to an undesirable value or set (which may or may not be known to system operators) via a local actuation. We evaluate the network vulnerability in terms of the whether or not the intruder can achieve its goal, and also the minimum actuation energy (or expected minimum energy, if the goal is unknown) required of the adversary to achieve the goal. We briefly provide graphical conditions for whether or not the intruder can achieve its goal, but primarily focus on characterizing the energy required for intrusion. To this end, we formalize that the required energy is related to the inverse of the controllability Gramian for the process, and statistics defined thereof (e.g., its trace and determinant). We then obtain explicit formulas for the Gramian inverse and its associated statistics, by drawing on the inversion formula for Cauchy matrices. These explicit formulae yield interesting structural and graph-theoretic characterizations of

[1]  H. Neudecker,et al.  Block Kronecker products and the vecb operator , 1991 .

[2]  S. Strogatz.  From Kuramoto to Crawford: exploring the onset of synchronization in populations of coupled oscillators , 2000 .

[3]  Albert-László Barabási,et al.  Scale-Free Networks: A Decade and Beyond , 2009, Science.

[4]  F. Bullo,et al.  Topological equivalence of a structure-preserving power network model and a non-uniform Kuramoto model of coupled oscillators , 2011, IEEE Conference on Decision and Control and European Control Conference.

[5]  David A. Clark.  INVESTIGATING A NEW GROUND DELAY PROGRAM STRATEGY FOR COPING WITH SFO STRATUS * , 2009 .

[6]  Chalee Asavathiratham,et al.  The influence model: a tractable representation for the dynamics of networked Markov chains , 2001 .

[7]  Sandip Roy,et al.  A Scalable Methodology For Evaluating And Designing Coordinated Air Traffic Flow Management Strategies Under Uncertainty , 2007 .

[8]  Ivan Stojmenovic,et al.  Guest Editorial Special Issue on Wireless Sensor and Actuator Networks , 2011 .

[9]  J.J. Gertler,et al.  Survey of model-based failure detection and isolation in complex plants , 1988, IEEE Control Systems Magazine.

[10]  T. Basar,et al.  A game theoretic approach to decision and analysis in network intrusion detection , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[11]  Yan Wan,et al.  Majorizations for the dominant eigenvector of a nonnegative matrix , 2008, 2008 American Control Conference.

[12]  Cristinel Ababei.  Network on chip design and optimization using specialized influence models , 2010, Design Automation Conference.

[13]  Victor M. Preciado.  Spectral analysis for stochastic models of large-scale complex dynamical networks , 2008 .

[14]  W. Rugh.  Linear System Theory , 1992 .

[15]  M.L.J. Hautus,et al.  Controllability and observability conditions of linear autonomous systems , 1969 .

[16]  Florian Dörfler,et al.  Cyber-physical attacks in power networks: Models, fundamental limitations and monitor design , 2011, IEEE Conference on Decision and Control and European Control Conference.

[17]  Sandip Roy,et al.  Performance analysis of an influence-model-based graph partitioning algorithm , 2011, IEEE Conference on Decision and Control and European Control Conference.

[18]  A. C. Rencher.  Linear models in statistics , 1999 .

[19]  H. Happ.  Power system control and stability , 1979, Proceedings of the IEEE.

[20]  Kapil Sheth,et al.  Aggregate Flow Model for Air-Traffic Management , 2004 .

[21]  Ross A. Malaga.  Search Engine Optimization - Black and White Hat Approaches , 2010, Adv. Comput..

[22]  Sandip Roy,et al.  A Stochastic Spatiotemporal Weather-Impact Simulator: Representative Scenario Selection , 2011 .

[23]  Chinwendu Enyioha,et al.  Optimal Resource Allocation for Network Protection: A Geometric Programming Approach , 2013, ArXiv.

[24]  Stephen P. Boyd,et al.  Distributed average consensus with least-mean-square deviation , 2007, J. Parallel Distributed Comput..

[25]  Sandip Roy,et al.  Moment-linear stochastic systems and their applications , 2003 .

[26]  Michael Stiebitz,et al.  An historical note: Euler's Königsberg letters , 1988, J. Graph Theory.

[27]  Yi Zhou,et al.  Dynamic Queuing Network Model for Flow Contingency Management , 2011, IEEE Transactions on Intelligent Transportation Systems.

[28]  Siddhartha Sahi.  Logarithmic convexity of Perron-Frobenius eigenvectors of positive matrices , 1993 .

[29]  Sajal K. Das,et al.  Security and vulnerability of cyber-physical infrastructure networks: A control-theoretic approach , 2012 .

[30]  André Teixeira,et al.  Networked control systems under cyber attacks with applications to power networks , 2010, Proceedings of the 2010 American Control Conference.

[31]  Malur K. Sundareshan,et al.  Numerical Methods for Modeling Computer Networks Under Nonstationary Conditions , 1990, IEEE J. Sel. Areas Commun..

[32]  S. Boccaletti,et al.  Synchronization of chaotic systems , 2001 .

[33]  David Ward,et al.  Vulnerable links and secure architectures in the stabilization of networks of controlled dynamical systems , 2012, 2012 American Control Conference (ACC).

[34]  Sandip Roy,et al.  Scaling: a canonical design problem for networks , 2006, 2006 American Control Conference.

[35]  Britta Ruhnau,et al.  Eigenvector-centrality - a node-centrality? , 2000, Soc. Networks.

[36]  Hamsa Balakrishnan,et al.  Estimation of maximum-likelihood discrete-choice models of the runway configuration selection process , 2011, Proceedings of the 2011 American Control Conference.

[37]  Mauricio Barahona,et al.  Synchronization in small-world systems. , 2002, Physical review letters.

[38]  Stephen Atkins.  Toward System Oriented Runway Management , 2010, 29th Digital Avionics Systems Conference.

[39]  Sandip Roy,et al.  Vulnerability of continuous-time network synchronization processes: A minimum energy perspective , 2013, 52nd IEEE Conference on Decision and Control.

[40]  R. Merris.  Laplacian graph eigenvectors , 1998 .

[41]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[42]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[43]  K. Loparo,et al.  Stochastic stability properties of jump linear systems , 1992 .

[44]  Frank Harary,et al.  Graph Theory , 2016 .

[45]  S. Strogatz.  Exploring complex networks , 2001, Nature.

[46]  John-Paul Clarke,et al.  A probabilistic decision-making model for runway configuration planning under stochastic wind conditions , 2009, 2009 IEEE/AIAA 28th Digital Avionics Systems Conference.

[47]  Gano B. Chatterji,et al.  ANALYSIS OF AIRCRAFT ARRIVAL AND DEPARTURE DELAY CHARACTERISTICS , 2002 .

[48]  Eugene P. Gilbo,et al.  Airport capacity: representation, estimation, optimization , 1993, IEEE Trans. Control. Syst. Technol..

[49]  Carl M. Harris,et al.  Fundamentals of queueing theory , 1975 .

[50]  Ιωαννησ Τσιτσικλησ,et al.  PROBLEMS IN DECENTRALIZED DECISION MAKING AND COMPUTATION , 1984 .

[51]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

[52]  P. Erdos,et al.  On the evolution of random graphs , 1984 .

[53]  Banavar Sridhar,et al.  Modeling and Optimization in Traffic Flow Management , 2008, Proceedings of the IEEE.

[54]  Krishnakumar Ramamoorthy,et al.  An Empirical Airport Configuration Prediction Model , 2012 .

[55]  S. Roy,et al.  A control-theoretic perspective on the design of distributed agreement protocols , 2005, Proceedings of the 2005, American Control Conference, 2005..

[56]  Sujata Banerjee,et al.  A simple approximation for modeling nonstationary queues , 1996, Proceedings of IEEE INFOCOM '96. Conference on Computer Communications.

[57]  Francesco Bullo,et al.  Controllability Metrics, Limitations and Algorithms for Complex Networks , 2013, IEEE Transactions on Control of Network Systems.

[58]  Henry Stark,et al.  Probability, Random Processes, and Estimation Theory for Engineers , 1995 .

[59]  Sandip Roy,et al.  Forecasting Weather-Impacted Airport Capacities for Flow Contingency Management: Advanced Methods and Integration , 2013 .

[60]  Sandip Roy,et al.  Using Stochastic , Dynamic Weather-Impact Models in Strategic Traffic Flow Management , 2011 .

[61]  Dou Long,et al.  Progress Toward Future Runway Management , 2011 .

[62]  A. Saberi,et al.  Designing spatially heterogeneous strategies for control of virus spread. , 2008, IET systems biology.

[63]  Rajeev Motwani,et al.  The PageRank Citation Ranking : Bringing Order to the Web , 1999, WWW 1999.

[64]  Éva Tardos,et al.  Maximizing the Spread of Influence through a Social Network , 2015, Theory Comput..

[65]  Charles R. Johnson,et al.  Topics in Matrix Analysis , 1991 .

[66]  Sajal K. Das,et al.  Security and Discoverability of Spread Dynamics in Cyber-Physical Networks , 2012, IEEE Transactions on Parallel and Distributed Systems.

[67]  Antonio Bicchi,et al.  Distributed intrusion detection for secure consensus computations , 2007, 2007 46th IEEE Conference on Decision and Control.

[68]  Christoforos N. Hadjicostis,et al.  Privacy-preserving asymptotic average consensus , 2013, 2013 European Control Conference (ECC).

[69]  G. Verghese,et al.  An Aggregate Dynamic Stochastic Model for an Air Traffic System , 2002 .

[70]  John-Paul Clarke,et al.  Runway Operations Planning and Control: Sequencing and Scheduling , 2001 .

[71]  Varun Ramanujam,et al.  Estimation and tactical allocation of airport capacity in the presence of uncertainty , 2011 .

[72]  A. Bergen,et al.  Stability of systems with randomly time-varying parameters , 1960 .

[73]  Magnus Egerstedt,et al.  Controllability of Multi-Agent Systems from a Graph-Theoretic Perspective , 2009, SIAM J. Control. Optim..

[74]  Matthias Steiner,et al.  Integration of Probabilistic Weather Information with Air Traffic Management Decision-Making Tools—A Conceptual Vision for the Future , 2007 .

[75]  Randal W. Beard,et al.  Consensus seeking in multiagent systems under dynamically changing interaction topologies , 2005, IEEE Transactions on Automatic Control.

[76]  Stephen P. Boyd,et al.  Fast linear iterations for distributed averaging , 2003, 42nd IEEE International Conference on Decision and Control (IEEE Cat. No.03CH37475).

[77]  B. Bollobás.  The evolution of random graphs , 1984 .

[78]  Marios M. Polycarpou,et al.  Distributed Fault Detection and Isolation of Large-Scale Discrete-Time Nonlinear Systems: An Adaptive Approximation Approach , 2012, IEEE Transactions on Automatic Control.

[79]  Sandip Roy,et al.  Cramer-Rao bounds on eigenvalue estimates from impulse response data: The multi-observation case , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[80]  Sandip Roy,et al.  A Stochastic Network Model for Uncertain Spatiotemporal Weather Impact at the Strategic Time Horizon , 2010 .

[81]  Sandip Roy,et al.  Initial-Condition Estimation in Network Synchronization Processes: Algebraic and Graphical Characterizations of the Estimator , 2011, Complex Syst..

[82]  G. Stewart,et al.  Matrix Perturbation Theory , 1990 .

[83]  A. Berman,et al.  SEMIGROUPS OF NONNEGATIVE MATRICES , 1979 .

[84]  Richard A. Brualdi,et al.  Combinatorial verification of the elementary divisors of tensor products , 1985 .

[85]  Sandip Roy,et al.  Refinement and Enhancement of an Influence-Model-based Weather-Impact Simulator , 2012 .

[86]  Chih-Wei Chen,et al.  State detection from local measurements in network synchronization processes , 2013, 2013 American Control Conference.

[87]  H.G. Tanner,et al.  On the controllability of nearest neighbor interconnections , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[88]  Matthias Steiner,et al.  Airport Capacity Prediction Integrating Ensemble Weather Forecasts , 2012, Infotech@Aerospace.

[89]  D. Bernstein.  Matrix Mathematics: Theory, Facts, and Formulas , 2009 .

[90]  Jimmy Krozel,et al.  Strategic Traffic Flow Management Concept of Operations , 2004 .

[91]  M Chavez,et al.  Synchronization in complex networks with age ordering. , 2005, Physical review letters.

[92]  Sandip Roy.  Generating Representative Weather-Impact Futures for Strategic Traffic Flow Management , 2013 .

[93]  Mark Hansen,et al.  Generating Probabilistic Capacity Profiles from weather forecast: A design-of-experiment approach , 2011 .

[94]  A. Berman,et al.  Nonnegative matrices in dynamic systems , 1979 .

[95]  Sandip Roy,et al.  A new focus in the science of networks: towards methods for design , 2008, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[96]  Karl Henrik Johansson,et al.  Cyber security analysis of state estimators in electric power systems , 2010, 49th IEEE Conference on Decision and Control (CDC).

[97]  Gabrielle Demange,et al.  A Survey of Network Formation Models: Stability and Efficiency , 2005 .

[98]  T. Basar,et al.  A game theoretic analysis of intrusion detection in access control systems , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[99]  Sandip Roy,et al.  Layered Moment-Linear Network Models as Tools for Strategic Air Traffic Flow Management , 2012, Infotech@Aerospace.

[100]  Karl Henrik Johansson,et al.  Efficient Computations of a Security Index for False Data Attacks in Power Networks , 2012, IEEE Transactions on Automatic Control.

[101]  Ralph Langner,et al.  Stuxnet: Dissecting a Cyberwarfare Weapon , 2011, IEEE Security & Privacy.

[102]  Sandip Roy,et al.  Security concepts for the dynamics of autonomous vehicle networks , 2014, Autom..

[103]  J. Kleinfeld.  COULD IT BE A BIG WORLD AFTER ALL? THE "SIX DEGREES OF SEPARATION" MYTH , 2002 .

[104]  S. Sharma,et al.  Approximate models for the study of nonstationary queues and their applications to communication networks , 1993, Proceedings of ICC '93 - IEEE International Conference on Communications.

[105]  Huibert Kwakernaak,et al.  Linear Optimal Control Systems , 1972 .

[106]  Karl Henrik Johansson,et al.  Estimation over heterogeneous sensor networks , 2008, 2008 47th IEEE Conference on Decision and Control.

[107]  D. Spielman.  Algorithms, Graph Theory, and Linear Equations in Laplacian Matrices , 2011 .

[108]  Sandip Roy,et al.  Resource allocation in networks: a case study of the influence model , 2002, Proceedings of the 35th Annual Hawaii International Conference on System Sciences.

[109]  Antonio Bicchi,et al.  Consensus Computation in Unreliable Networks: A System Theoretic Approach , 2010, IEEE Transactions on Automatic Control.

[110]  Sandip Roy,et al.  On inference of network time constants from impulse response data: graph-theoretic Cramer-Rao bounds , 2009, Proceedings of the 48h IEEE Conference on Decision and Control (CDC) held jointly with 2009 28th Chinese Control Conference.

[111]  John G. Proakis,et al.  Probability, random variables and stochastic processes , 1985, IEEE Trans. Acoust. Speech Signal Process..

[112]  Daniel Murphy,et al.  Predicting Runway Configurations at Airports , 2012 .

[113]  Siddhartha Sahi,et al.  A note on the resolvent of a nonnegative matrix and its applications , 2010 .

[114]  Sandip Roy,et al.  Cost of fairness in disease spread control , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[115]  Gary W. Lohr,et al.  Current Practices in Runway Configuration Management (RCM) and Arrival/Departure Runway Balancing (ADRB) , 2008 .

[116]  Sandip Roy,et al.  A Framework for Flow Contingency Management , 2011 .

[117]  Jurgen Kurths,et al.  Synchronization in complex networks , 2008, 0805.2976.

[118]  Sandip Roy,et al.  The influence model , 2001 .

[119]  Robert G. Gallager,et al.  Discrete Stochastic Processes , 1995 .

[120]  John N. Tsitsiklis,et al.  Convergence Speed in Distributed Consensus and Averaging , 2009, SIAM J. Control. Optim..

[121]  M. Fiedler.  A property of eigenvectors of nonnegative symmetric matrices and its application to graph theory , 1975 .

[122]  Karl Henrik Johansson,et al.  A Cyber Security Study of a SCADA Energy Management System: Stealthy Deception Attacks on the State Estimator , 2010, ArXiv.

[123]  Yan Wan,et al.  The impact of multi‐group multi‐layer network structure on the performance of distributed consensus building strategies , 2013 .

[124]  F. Bullo,et al.  A graph-theoretical characterization of power network vulnerabilities , 2011, Proceedings of the 2011 American Control Conference.