Almost Sure Stability of Nonlinear Systems Under Random and Impulsive Sequential Attacks

This article is concerned with the stability problem for a class of Lipschitz-type nonlinear systems in networked environments, which are suffered from random and impulsive deception attacks. The attack is modeled as a randomly destabilizing impulsive sequence, whose impulsive instants and impulsive gains are both random with only the expectations available. Almost sure stability is ensured based on Doob's Martingale Convergence Theorem. Sufficient conditions are derived for the solution of the nonlinear system to be almost surely stable. An example is given to verify the effectiveness of the theoretical results. It is shown that the random attack will be able to destroy the stability, therefore, a large feedback gain may be necessary.

[1]  Feng Qian,et al.  Network-based leader-following consensus of nonlinear multi-agent systems via distributed impulsive control , 2017, Inf. Sci..

[2]  R. Durrett Probability: Theory and Examples , 1993 .

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

[4]  Ling Shi,et al.  Optimal Linear Cyber-Attack on Remote State Estimation , 2017, IEEE Transactions on Control of Network Systems.

[5]  John Y. Hung,et al.  Denial of service attacks on network-based control systems: impact and mitigation , 2005, IEEE Transactions on Industrial Informatics.

[6]  Zhong-Hua Pang,et al.  Secure Networked Control Systems under Denial of Service Attacks , 2011 .

[7]  Fan Zhang,et al.  Dynamic Feedback Synchronization of Lur'e Networks via Incremental Sector Boundedness , 2016, IEEE Transactions on Automatic Control.

[8]  Guanrong Chen,et al.  Stability of Switched Systems on Randomly Switching Durations With Random Interaction Matrices , 2018, IEEE Transactions on Automatic Control.

[9]  Daniel W. C. Ho,et al.  Observer-Based Event-Triggering Consensus Control for Multiagent Systems With Lossy Sensors and Cyber-Attacks , 2017, IEEE Transactions on Cybernetics.

[10]  Panos J. Antsaklis,et al.  Risk-Sensitive Control Under Markov Modulated Denial-of-Service (DoS) Attack Strategies , 2015, IEEE Transactions on Automatic Control.

[11]  Qing-Long Han,et al.  State estimation under false data injection attacks: Security analysis and system protection , 2018, Autom..

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

[13]  Bruno Sinopoli,et al.  Integrity Data Attacks in Power Market Operations , 2011, IEEE Transactions on Smart Grid.

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

[15]  Xi Chen,et al.  Robust input-to-output stabilization of nonlinear systems , 2016, WCICA 2016.

[16]  Feng Qian,et al.  Secure impulsive synchronization control of multi-agent systems under deception attacks , 2018, Inf. Sci..

[17]  Qing-Long Han,et al.  Adaptive Consensus Control of Linear Multiagent Systems With Dynamic Event-Triggered Strategies , 2020, IEEE Transactions on Cybernetics.

[18]  Jiming Chen,et al.  Analysis of Consensus-Based Distributed Economic Dispatch Under Stealthy Attacks , 2017, IEEE Transactions on Industrial Electronics.

[19]  Tao Yang,et al.  In: Impulsive control theory , 2001 .

[20]  Jiming Chen,et al.  Learning-Based Jamming Attack against Low-Duty-Cycle Networks , 2017, IEEE Transactions on Dependable and Secure Computing.

[21]  Xiaodi Li,et al.  Stabilization of Delay Systems: Delay-Dependent Impulsive Control , 2017, IEEE Transactions on Automatic Control.

[22]  Laurentiu Hetel,et al.  Nonlinear impulsive systems: 2D stability analysis approach , 2017, Autom..

[23]  Jie Huang,et al.  Stabilization and Regulation of Nonlinear Systems , 2015 .

[24]  Jinde Cao,et al.  A unified synchronization criterion for impulsive dynamical networks , 2010, Autom..

[25]  Ing-Ray Chen,et al.  Effect of Intrusion Detection and Response on Reliability of Cyber Physical Systems , 2013, IEEE Transactions on Reliability.

[26]  James Lam,et al.  Quasi-synchronization of heterogeneous dynamic networks via distributed impulsive control: Error estimation, optimization and design , 2015, Autom..

[27]  Daoyi Xu,et al.  Stability Analysis of Delay Neural Networks With Impulsive Effects , 2005, IEEE Trans. Circuits Syst. II Express Briefs.

[28]  Tansel Yucelen,et al.  An Adaptive Control Architecture for Mitigating Sensor and Actuator Attacks in Cyber-Physical Systems , 2017, IEEE Transactions on Automatic Control.

[29]  Wei Xing Zheng,et al.  Impulsive stabilization of a class of singular systems with time-delays , 2017, Autom..