Fundamental Stealthiness-Distortion Tradeoffs in Dynamical (Control) Systems under Injection Attacks: A Power Spectral Analysis

In this paper, we analyze the fundamental stealthiness-distortion tradeoffs of linear Gaussian open-loop dynamical systems and (closed-loop) feedback control systems under data injection attacks using a power spectral analysis, whereas the Kullback-Leibler (KL) divergence is employed as the stealthiness measure. Particularly, we obtain explicit formulas in terms of power spectra that characterize analytically the stealthiness-distortion tradeoffs as well as the properties of the worst-case attacks. Furthermore, it is seen in general that the attacker only needs to know the input-output behaviors of the systems in order to carry out the worst-case attacks.

[1]  Huaiyu Zhu.  On Information and Sufficiency , 1997 .

[2]  U. Grenander,et al.  Toeplitz Forms And Their Applications , 1958 .

[3]  Amiel Feinstein,et al.  Information and information stability of random variables and processes , 1964 .

[4]  Paulo Tabuada,et al.  Guest Editorial Special Issue on Control of Cyber-Physical Systems , 2014, IEEE Trans. Autom. Control..

[5]  Petre Stoica,et al.  Spectral Analysis of Signals , 2009 .

[6]  Bruno Sinopoli,et al.  Resilient Control in Cyber-Physical Systems: Countering Uncertainty, Constraints, and Adversarial Behavior , 2019, Found. Trends Syst. Control..

[7]  Henrik Sandberg,et al.  A Tutorial Introduction to Security and Privacy for Cyber-Physical Systems , 2019, 2019 18th European Control Conference (ECC).

[8]  H. Vincent Poor,et al.  An Introduction to Signal Detection and Estimation , 1994, Springer Texts in Electrical Engineering.

[9]  Ling Shi,et al.  Worst-case stealthy innovation-based linear attack on remote state estimation , 2018, Autom..

[10]  Sandeep K. S. Gupta,et al.  Special Issue on Cyber-Physical Systems [Scanning the Issue] , 2012, Proc. IEEE.

[11]  Vijay Gupta,et al.  Data-injection attacks in stochastic control systems: Detectability and performance tradeoffs , 2017, Autom..

[12]  Lennart Ljung,et al.  System Identification: Theory for the User , 1987 .

[13]  Johan Karlsson,et al.  Metrics for Power Spectra: An Axiomatic Approach , 2009, IEEE Transactions on Signal Processing.

[14]  Pedro M. Crespo,et al.  Asymptotically Equivalent Sequences of Matrices and Hermitian Block Toeplitz Matrices With Continuous Symbols: Applications to MIMO Systems , 2008, IEEE Transactions on Information Theory.

[15]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[16]  Michele Pavon,et al.  Time and Spectral Domain Relative Entropy: A New Approach to Multivariate Spectral Estimation , 2011, IEEE Transactions on Automatic Control.

[17]  Karl Henrik Johansson,et al.  Cyberphysical Security in Networked Control Systems: An Introduction to the Issue , 2015 .

[18]  Ruochi Zhang,et al.  Stealthy Control Signal Attacks in Linear Quadratic Gaussian Control Systems: Detectability Reward Tradeoff , 2017, IEEE Transactions on Information Forensics and Security.

[19]  M. Pirani,et al.  A systems and control perspective of CPS security , 2019, Annu. Rev. Control..

[20]  Fatos Xhafa,et al.  Special issue on cyber physical systems , 2013, Computing.

[21]  G. Picci,et al.  Linear Stochastic Systems: A Geometric Approach to Modeling, Estimation and Identification , 2016 .

[22]  Quanyan Zhu,et al.  Independent Gaussian Distributions Minimize the Kullback-Leibler (KL) Divergence from Independent Gaussian Distributions , 2020, ArXiv.

[23]  Vijay Gupta,et al.  On Kalman Filtering with Compromised Sensors: Attack Stealthiness and Performance Bounds , 2017, IEEE Transactions on Automatic Control.

[24]  Ling Shi,et al.  Guest Editorial Special Issue on Secure Control of Cyber-Physical Systems , 2017, IEEE Trans. Control. Netw. Syst..

[25]  L. Pardo.  Statistical Inference Based on Divergence Measures , 2005 .

[26]  J. H. van Schuppen,et al.  System identification with information theoretic criteria , 1995 .