A secure state estimation algorithm for nonlinear systems under sensor attacks

The state estimation of continuous-time nonlinear systems in which a subset of sensor outputs can be maliciously controlled through injecting a potentially unbounded additive signal is considered in this paper. Analogous to our earlier work for continuous-time linear systems in \cite{chong2015observability}, we term the convergence of the estimates to the true states in the presence of sensor attacks as `observability under $M$ attacks', where $M$ refers to the number of sensors which the attacker has access to. Unlike the linear case, we only provide a sufficient condition such that a nonlinear system is observable under $M$ attacks. The condition requires the existence of asymptotic observers which are robust with respect to the attack signals in an input-to-state stable sense. We show that an algorithm to choose a compatible state estimate from the state estimates generated by the bank of observers achieves asymptotic state reconstruction. We also provide a constructive method for a class of nonlinear systems to design state observers which have the desirable robustness property. The relevance of this study is illustrated on monitoring the safe operation of a power distribution network.Comment: This paper has been accepted for publication at the 59th IEEE Conference on Decision and Control, 202

Co-design of Control and Scheduling in Networked Systems under Denial-of-Service attacks

We consider the joint design of control and scheduling under stochastic Denial-of-Service (DoS) attacks in the context of networked control systems. A sensor takes measurements of the system output and forwards its dynamic state estimates to a remote controller over a packet-dropping link. The controller determines the optimal control law for the process using the estimates it receives. An attacker aims at degrading the control performance by increasing the packet-dropout rate with a DoS attack towards the sensor-controller channel. Assume both the controller and the attacker are rational in a game-theoretic sense. We establish a partially observable stochastic game to derive the optimal joint design of scheduling and control. Using dynamic programming we prove that the control and scheduling policies can be designed separately without sacrificing optimality, making the problem equivalent to a complete information game. We employ Nash Q-learning to solve the problem and prove that the solution is guaranteed to constitute an $\epsilon$-Nash equilibrium. Numerical examples are provided to illustrate the tradeoffs between control performance and communication cost.Comment: 9 pages, 4 figure

Stealthy hacking and secrecy of controlled state estimation systems with random dropouts

We study the maximum information gain that an adversary may obtain through hacking without being detected. Consider a dynamical process observed by a sensor that transmits a local estimate of the system state to a remote estimator according to some reference transmission policy across a packet-dropping wireless channel equipped with acknowledgments (ACK). An adversary overhears the transmissions and proactively hijacks the sensor to reprogram its transmission policy. We define perfect secrecy as keeping the averaged expected error covariance bounded at the legitimate estimator and unbounded at the adversary. By analyzing the stationary distribution of the expected error covariance, we show that perfect secrecy can be attained for unstable systems only if the ACK channel has no packet dropouts. In other situations, we prove that independent of the reference policy and the detection methods, perfect secrecy is not attainable. For this scenario, we formulate a constrained Markov decision process to derive the optimal transmission policy that the adversary should implement at the sensor, and devise a Stackelberg game to derive the optimal reference policy for the legitimate estimator.Comment: 16 pages, 6 figure

Learning-based Attacks in Cyber-Physical Systems

We introduce the problem of learning-based attacks in an abstraction of cyber-physical systems that may be subject to an attack that overrides the sensor readings and the controller actions. The attacker attempts to learn the dynamics of the plant and subsequently override the controller's actuation signal, to destroy the plant without being detected. The attacker can feed fictitious sensor readings to the controller using its estimate of the plant dynamics and mimic the legitimate plant operation. The controller, on the other hand, is constantly on the lookout for an attack; once the controller detects an attack, it immediately shuts the plant off. We derive lower bounds for the attacker's deception probability for linear plants by assuming a specific authentication test that inspects the empirical variance of the system disturbance. We also show how the controller can improve the security of the system by superimposing a carefully crafted privacy-enhancing signal on top of the control policy. Finally, for nonlinear scalar dynamics that belong to the Reproducing Kernel Hilbert Space, we investigate the performance of attacks based on Gaussian-processes regression