Risk Assessment of Stealthy Attacks on Uncertain Control Systems

In this article, we address the problem of risk assessment of stealthy attacks on uncertain control systems. Considering data injection attacks that aim at maximizing impact while remaining undetected, we use the recently proposed output-to-output gain to characterize the risk associated with the impact of attacks under a limited system knowledge attacker. The risk is formulated using a well-established risk metric, namely the maximum expected loss. Under this setups, the risk assessment problem corresponds to an untractable infinite non-convex optimization problem. To address this limitation, we adopt the framework of scenario-based optimization to approximate the infinite non-convex optimization problem by a sampled non-convex optimization problem. Then, based on the framework of dissipative system theory and S-procedure, the sampled non-convex risk assessment problem is formulated as an equivalent convex semi-definite program. Additionally, we derive the necessary and sufficient conditions for the risk to be bounded. Finally, we illustrate the results through numerical simulation of a hydro-turbine power system

On Kalman Filtering over Fading Wireless Channels with Controlled Transmission Powers

We study stochastic stability of centralized Kalman filtering for linear time-varying systems equipped with wireless sensors. Transmission is over fading channels where variable channel gains are counteracted by power control to alleviate the effects of packet drops. We establish sufficient conditions for the expected value of the Kalman filter covariance matrix to be exponentially bounded in norm. The conditions obtained are then used to formulate stabilizing power control policies which minimize the total sensor power budget. In deriving the optimal power control laws, both statistical channel information and full channel information are considered. The effect of system instability on the power budget is also investigated for both these cases

Quantized Non-Bayesian Quickest Change Detection with Energy Harvesting

This paper focuses on the analysis of an optimal sensing and quantization strategy in a multi-sensor network where each individual sensor sends its quantized log-likelihood information to the fusion center (FC) for non-Bayesian quickest change detection. It is assumed that the sensors are equipped with a battery/energy storage device of finite capacity, capable of harvesting energy from the environment. The FC is assumed to have access to either non-causal or causal channel state information (CSI) and energy state information (ESI) from all the sensors while performing the quickest change detection. The primary observations are assumed to be generated from a sequence of random variables whose probability distribution function changes at an unknown time point. The objective of the detection problem is to minimize the average detection delay of the change point with respect to a lower bound on the rate of false alarm. In this framework, the optimal sensing decision and number of quantization bits for information transmission can be determined with the constraint of limited available energy due to finite battery capacity. This optimization is formulated as a stochastic control problem and is solved using dynamic programming algorithms for both non-causal and causal CSI and ESI scenario. A set of non-linear equations is also derived to determine the optimal quantization thresholds for the sensor log-likelihood ratios, by maximizing an appropriate Kullback-Leibler (KL) divergence measure between the distributions before and after the change. A uniform threshold quantization strategy is also proposed as a simple sub-optimal policy. The simulation results indicate that the optimal quantization is preferable when the number of quantization bits is low as its performance is significantly better compared to its uniform counterpart in terms of average detection delay. For the case of a large number of quantization bits, the performance benefits of using the optimal quantization as compared to its uniform counterpart diminish, as expected

Wiener Filter Design Using Polynomial Equations

A simplified way of deriving of realizable and explicit Wiener filters is presented. Discrete time problems are discussed, in a polynomial equation framework. Optimal filters, predictors and smoothers are calculated by means of spectral factorizations and linear polynomial equations. A new tool for obtaining these equations, for a given problem structure, is described. It is based on evaluation of orthogonality in the frequency domain, by means of cancelling stable poles with zeros. Comparisons are made to previously known derivation methodology such as "completing the squares" for the polynomial systems approach and the classical Wiener solution. The simplicity of the proposed derivation method is particularly evident in multisignal filtering problems. To illustrate, two examples are discussed: a filtering and a generalized deconvolution problem. A new solvability condition for linear polynomial equations appearing in scalar problems is also presented. EDICS no. 4.2.2. Keywords: Wiene..