A Graph-Theoretic Characterization of Perfect Attackability for Secure Design of Distributed Control Systems

This paper considers secure design in distributed control systems to ensure the detection of stealthy integrity attacks. Distributed control systems consist of many heterogeneous components, such as sensors, controllers, and actuators and may contain several independent agents. The presence of many components and agents in a system increases the attack surfaces for potential adversaries, making distributed control systems vulnerable to malicious behavior. The goal of this paper is to consider the design of distributed control systems to ensure the deterministic detection of attacks. To do this, we leverage existing results which relate the deterministic detection of a fixed set of malicious nodes to structural left invertibility. We extend the notion of structural left invertibility to consider attacks from all possible sets of malicious nodes using vertex separators. Vertex separators are then used to solve optimization problems which aim to minimize communication networks while also ensuring that a resource limited adversary cannot generate perfect attacks. Optimal bounds on communication and sensing are obtained and polynomial time design algorithms are provided.

[1]  Yilin Mo,et al.  False Data Injection Attacks in Control Systems , 2010 .

[2]  Paulo Tabuada,et al.  Robustness of attack-resilient state estimators , 2014, 2014 ACM/IEEE International Conference on Cyber-Physical Systems (ICCPS).

[3]  S. E. Schaeffer.  Survey Graph clustering , 2007 .

[4]  Frede Blaabjerg,et al.  Overview of Control and Grid Synchronization for Distributed Power Generation Systems , 2006, IEEE Transactions on Industrial Electronics.

[5]  Randal W. Beard,et al.  Distributed Consensus in Multi-vehicle Cooperative Control - Theory and Applications , 2007, Communications and Control Engineering.

[6]  B.F. Wollenberg,et al.  Toward a smart grid: power delivery for the 21st century , 2005, IEEE Power and Energy Magazine.

[7]  Shreyas Sundaram,et al.  The wireless control network: Monitoring for malicious behavior , 2010, 49th IEEE Conference on Decision and Control (CDC).

[8]  Yilin Mo,et al.  Dynamic state estimation in the presence of compromised sensory data , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[9]  Soummya Kar,et al.  Minimum Sensor Placement for Robust Observability of Structured Complex Networks , 2015, ArXiv.

[10]  Bruno Sinopoli,et al.  A graph theoretic characterization of perfect attackability and detection in Distributed Control Systems , 2015, 2016 American Control Conference (ACC).

[11]  Robert E. Tarjan,et al.  Network Flow and Testing Graph Connectivity , 1975, SIAM J. Comput..

[12]  Richard M. Murray,et al.  DISTRIBUTED COOPERATIVE CONTROL OF MULTIPLE VEHICLE FORMATIONS USING STRUCTURAL POTENTIAL FUNCTIONS , 2002 .

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

[14]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[15]  Karl Henrik Johansson,et al.  On Security Indices for State Estimators in Power Networks , 2010 .

[16]  Soummya Kar,et al.  A Framework for Structural Input/Output and Control Configuration Selection in Large-Scale Systems , 2013, IEEE Transactions on Automatic Control.

[17]  Bruno Sinopoli,et al.  Distributed control applications within sensor networks , 2003, Proc. IEEE.

[18]  S. Shankar Sastry,et al.  Secure Control: Towards Survivable Cyber-Physical Systems , 2008, 2008 The 28th International Conference on Distributed Computing Systems Workshops.

[19]  Ki-Won Yeom.  Distributed Formation Control for Communication Relay with Positionless Flying Agents , 2011, FGIT-MulGraB.

[20]  Ching-tai Lin.  Structural controllability , 1974 .

[21]  Jill Slay,et al.  Lessons Learned from the Maroochy Water Breach , 2007, Critical Infrastructure Protection.

[22]  Emanuele Garone,et al.  False data injection attacks against state estimation in wireless sensor networks , 2010, 49th IEEE Conference on Decision and Control (CDC).

[23]  Eric V. Denardo,et al.  Flows in Networks , 2011 .

[24]  Paulo Tabuada,et al.  Secure Estimation and Control for Cyber-Physical Systems Under Adversarial Attacks , 2012, IEEE Transactions on Automatic Control.

[25]  Bruno Sinopoli,et al.  Modeling impact of attacks, recovery, and attackability conditions for situational awareness , 2014, 2014 IEEE International Inter-Disciplinary Conference on Cognitive Methods in Situation Awareness and Decision Support (CogSIMA).

[26]  Florian Dörfler,et al.  Attack Detection and Identification in Cyber-Physical Systems -- Part II: Centralized and Distributed Monitor Design , 2012, ArXiv.

[27]  Peng Ning,et al.  False data injection attacks against state estimation in electric power grids , 2009, CCS.

[28]  Shreyas Sundaram,et al.  Distributed Function Calculation via Linear Iterative Strategies in the Presence of Malicious Agents , 2011, IEEE Transactions on Automatic Control.

[29]  K. Menger.  Zur allgemeinen Kurventheorie , 1927 .