A Satisfiability Modulo Theory Approach to Secure State Reconstruction in Differentially Flat Systems Under Sensor Attacks

Author(s): Shoukry, Yasser; Nuzzo, Pierluigi; Bezzo, Nicola; Sangiovanni-Vincentelli, Alberto L; Seshia, Sanjit A; Tabuada, Paulo | Abstract: We address the problem of estimating the state of a differentially flat system from measurements that may be corrupted by an adversarial attack. In cyber-physical systems, malicious attacks can directly compromise the system's sensors or manipulate the communication between sensors and controllers. We consider attacks that only corrupt a subset of sensor measurements. We show that the possibility of reconstructing the state under such attacks is characterized by a suitable generalization of the notion of s-sparse observability, previously introduced by some of the authors in the linear case. We also extend our previous work on the use of Satisfiability Modulo Theory solvers to estimate the state under sensor attacks to the context of differentially flat systems. The effectiveness of our approach is illustrated on the problem of controlling a quadrotor under sensor attacks.

[1]  M. Fliess,et al.  Flatness and defect of non-linear systems: introductory theory and examples , 1995 .

[2]  Paulo Tabuada,et al.  Secure State Estimation Under Sensor Attacks: A Satisfiability Modulo Theory Approach , 2014, ArXiv.

[3]  Sharad Malik,et al.  Boolean satisfiability from theoretical hardness to practical success , 2009, Commun. ACM.

[4]  脇元 修一,et al.  IEEE International Conference on Robotics and Automation (ICRA) におけるフルードパワー技術の研究動向 , 2011 .

[5]  Stephen P. Boyd,et al.  Real-Time Convex Optimization in Signal Processing , 2010, IEEE Signal Processing Magazine.

[6]  Vijay Kumar,et al.  The GRASP Multiple Micro-UAV Testbed , 2010, IEEE Robotics & Automation Magazine.

[7]  Raffaello D'Andrea,et al.  A simple learning strategy for high-speed quadrocopter multi-flips , 2010, 2010 IEEE International Conference on Robotics and Automation.

[8]  F. Bullo,et al.  Control-Theoretic Methods for Cyber-Physical Security , 2013 .

[9]  Peng Ning,et al.  False data injection attacks against state estimation in electric power grids , 2011, TSEC.

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

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

[12]  Paulo Tabuada,et al.  Sound and complete state estimation for linear dynamical systems under sensor attacks using Satisfiability Modulo Theory solving , 2015, 2015 American Control Conference (ACC).

[13]  Francesco Bullo,et al.  Control-Theoretic Methods for Cyberphysical Security: Geometric Principles for Optimal Cross-Layer Resilient Control Systems , 2015, IEEE Control Systems.

[14]  Paulo Tabuada,et al.  Event-triggered projected Luenberger observer for linear systems under sparse sensor attacks , 2014, 53rd IEEE Conference on Decision and Control.

[15]  S. Mitter,et al.  Robust Recursive Estimation in the Presence of Heavy-Tailed Observation Noise , 1994 .

[16]  Cesare Tinelli,et al.  Satisfiability Modulo Theories , 2021, Handbook of Satisfiability.

[17]  Paulo Tabuada,et al.  Event-Triggered State Observers for Sparse Sensor Noise/Attacks , 2013, IEEE Transactions on Automatic Control.

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

[19]  A. Sangiovanni-Vincentelli,et al.  I MHOTEP-SMT : A Satisfiability Modulo Theory Solver For Secure State Estimation ∗ , 2015 .

[20]  Vijay Gupta,et al.  On Kalman filtering in the presence of a compromised sensor: Fundamental performance bounds , 2014, 2014 American Control Conference.

[21]  João Pedro Hespanha,et al.  Observability of linear systems under adversarial attacks , 2015, 2015 American Control Conference (ACC).

[22]  Bruno Sinopoli,et al.  Secure Estimation in the Presence of Integrity Attacks , 2013, IEEE Transactions on Automatic Control.

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

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

[25]  Paulo Tabuada,et al.  Non-invasive Spoofing Attacks for Anti-lock Braking Systems , 2013, CHES.

[26]  Georgios B. Giannakis,et al.  Doubly Robust Smoothing of Dynamical Processes via Outlier Sparsity Constraints , 2011, IEEE Transactions on Signal Processing.