Characterization of Model-Based Detectors for CPS Sensor Faults/Attacks

A vector-valued model-based cumulative sum (CUSUM) procedure is proposed for identifying faulty/falsified sensor measurements. First, given the system dynamics, we derive tools for tuning the CUSUM procedure in the fault/attack free case to fulfill a desired detection performance (in terms of false alarm rate). We use the widely-used chi-squared fault/attack detection procedure as a benchmark to compare the performance of the CUSUM. In particular, we characterize the state degradation that a class of attacks can induce to the system while enforcing that the detectors (CUSUM and chi-squared) do not raise alarms. In doing so, we find the upper bound of state degradation that is possible by an undetected attacker. We quantify the advantage of using a dynamic detector (CUSUM), which leverages the history of the state, over a static detector (chi-squared) which uses a single measurement at a time. Simulations of a chemical reactor with heat exchanger are presented to illustrate the performance of our tools.Comment: Submitted to IEEE Transactions on Control Systems Technolog

Secure and Private Implementation of Dynamic Controllers Using Semi-Homomorphic Encryption

This paper presents a secure and private implementation of linear time-invariant dynamic controllers using Paillier's encryption, a semi-homomorphic encryption method. To avoid overflow or underflow within the encryption domain, the state of the controller is reset periodically. A control design approach is presented to ensure stability and optimize performance of the closed-loop system with encrypted controller.Comment: Improved numerical exampl

An Unknown Input Multi-Observer Approach for Estimation and Control under Adversarial Attacks

We address the problem of state estimation, attack isolation, and control of discrete-time linear time-invariant systems under (potentially unbounded) actuator and sensor false data injection attacks. Using a bank of unknown input observers, each observer leading to an exponentially stable estimation error (in the attack-free case), we propose an observer-based estimator that provides exponential estimates of the system state in spite of actuator and sensor attacks. Exploiting sensor and actuator redundancy, the estimation scheme is guaranteed to work if a sufficiently small subset of sensors and actuators are under attack. Using the proposed estimator, we provide tools for reconstructing and isolating actuator and sensor attacks; and a control scheme capable of stabilizing the closed-loop dynamics by switching off isolated actuators. Simulation results are presented to illustrate the performance of our tools.Comment: arXiv admin note: substantial text overlap with arXiv:1811.1015

Design-Time Quantification of Integrity in Cyber-Physical-Systems

In a software system it is possible to quantify the amount of information that is leaked or corrupted by analysing the flows of information present in the source code. In a cyber-physical system, information flows are not only present at the digital level, but also at a physical level, and to and fro the two levels. In this work, we provide a methodology to formally analyse a Cyber-Physical System composite model (combining physics and control) using an information flow-theoretic approach. We use this approach to quantify the level of vulnerability of a system with respect to attackers with different capabilities. We illustrate our approach by means of a water distribution case study

A Multi-Observer Based Estimation Framework for Nonlinear Systems under Sensor Attacks

We address the problem of state estimation and attack isolation for general discrete-time nonlinear systems when sensors are corrupted by (potentially unbounded) attack signals. For a large class of nonlinear plants and observers, we provide a general estimation scheme, built around the idea of sensor redundancy and multi-observer, capable of reconstructing the system state in spite of sensor attacks and noise. This scheme has been proposed by others for linear systems/observers and here we propose a unifying framework for a much larger class of nonlinear systems/observers. Using the proposed estimator, we provide an isolation algorithm to pinpoint attacks on sensors during sliding time windows. Simulation results are presented to illustrate the performance of our tools.Comment: arXiv admin note: text overlap with arXiv:1806.0648

Privacy Against Adversarial Classification in Cyber-Physical Systems

For a class of Cyber-Physical Systems (CPSs), we address the problem of performing computations over the cloud without revealing private information about the structure and operation of the system. We model CPSs as a collection of input-output dynamical systems (the system operation modes). Depending on the mode the system is operating on, the output trajectory is generated by one of these systems in response to driving inputs. Output measurements and driving inputs are sent to the cloud for processing purposes. We capture this "processing" through some function (of the input-output trajectory) that we require the cloud to compute accurately - referred here as the trajectory utility. However, for privacy reasons, we would like to keep the mode private, i.e., we do not want the cloud to correctly identify what mode of the CPS produced a given trajectory. To this end, we distort trajectories before transmission and send the corrupted data to the cloud. We provide mathematical tools (based on output-regulation techniques) to properly design distorting mechanisms so that: 1) the original and distorted trajectories lead to the same utility; and the distorted data leads the cloud to misclassify the mode

Improvement and analysis of a pseudo random bit generator by means of cellular automata

In this paper, we implement a revised pseudo random bit generator based on a rule-90 cellular automaton. For this purpose, we introduce a sequence matrix H_N with the aim of calculating the pseudo random sequences of N bits employing the algorithm related to the automaton backward evolution. In addition, a multifractal structure of the matrix H_N is revealed and quantified according to the multifractal formalism. The latter analysis could help to disentangle what kind of automaton rule is used in the randomization process and therefore it could be useful in cryptanalysis. Moreover, the conditions are found under which this pseudo random generator passes all the statistical tests provided by the National Institute of Standards and Technology (NIST)Comment: 20 pages, 12 figure

Synchronization in networks of diffusively coupled nonlinear systems:robustness against time-delays

In this manuscript, we study the problem of robust synchronization in networks of diffusively time-delayed coupled nonlinear systems. In particular, we prove that, under some mild conditions on the input-output dynamics of the systems and the network topology, there always exists a unimodal region in the parameter space (coupling strength versus time-delay), such that if they belong to this region, the systems synchronize. Moreover, we show how this unimodal region scales with the network topology, which, in turn, provides useful insights on how to design the network topology to maximize robustness against time-delays. The results are illustrated by extensive simulation experiments of time-delayed coupled Hindmarsh-Rose neural chaotic oscillators