Electrical and Electronic Engineering - Research Publications
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ItemOn Eigenvalues of Laplacian Matrix for a Class of Directed Signed Graphs( 2017-05-12)The eigenvalues of the Laplacian matrix for a class of directed graphs with both positive and negative weights are studied. First, a class of directed signed graphs is investigated in which one pair of nodes (either connected or not) is perturbed with negative weights. A necessary condition is proposed to attain the following objective for the perturbed graph: the real parts of the non-zero eigenvalues of its Laplacian matrix are positive. A sufficient condition is also presented that ensures the aforementioned objective for unperturbed graph. It is then highlighted the case where the condition becomes necessary and sufficient. Secondly, for directed graphs, a subset of pairs of nodes are identified where if any of the pairs is connected by an edge with infinitesimal negative weight, the resulting Laplacian matrix will have at least one eigenvalue with negative real part. Illustrative examples are presented to show the applicability of our results.
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ItemSecurity Metrics of Networked Control Systems under Sensor Attacks (extended preprint)( 2018-09-14)As more attention is paid to security in the context of control systems and as attacks occur to real control systems throughout the world, it has become clear that some of the most nefarious attacks are those that evade detection. The term stealthy has come to encompass a variety of techniques that attackers can employ to avoid being detected. In this manuscript, for a class of perturbed linear time-invariant systems, we propose two security metrics to quantify the potential impact that stealthy attacks could have on the system dynamics by tampering with sensor measurements. We provide analysis mathematical tools (in terms of linear matrix inequalities) to quantify these metrics for given system dynamics, control structure, system monitor, and set of sensors being attacked. Then, we provide synthesis tools (in terms of semidefinite programs) to redesign controllers and monitors such that the impact of stealthy attacks is minimized and the required attack-free system performance is guaranteed.
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ItemOn Privacy of Quantized Sensor Measurements through Additive Noise( 2018-09-10)We study the problem of maximizing privacy of quantized sensor measurements by adding random variables. In particular, we consider the setting where information about the state of a process is obtained using noisy sensor measurements. This information is quantized and sent to a remote station through an unsecured communication network. It is desired to keep the state of the process private; however, because the network is not secure, adversaries might have access to sensor information, which could be used to estimate the process state. To avoid an accurate state estimation, we add random numbers to the quantized sensor measurements and send the sum to the remote station instead. The distribution of these random variables is designed to minimize the mutual information between the sum and the quantized sensor measurements for a desired level of distortion -- how different the sum and the quantized sensor measurements are allowed to be. Simulations are presented to illustrate our results.
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ItemInformation-Theoretic Privacy through Chaos Synchronization and Optimal Additive Noise( 2019-06-03)We study the problem of maximizing privacy of data sets by adding random vectors generated via synchronized chaotic oscillators. In particular, we consider the setup where information about data sets, queries, is sent through public (unsecured) communication channels to a remote station. To hide private features (specific entries) within the data set, we corrupt the response to queries by adding random vectors. We send the distorted query (the sum of the requested query and the random vector) through the public channel. The distribution of the additive random vector is designed to minimize the mutual information (our privacy metric) between private entries of the data set and the distorted query. We cast the synthesis of this distribution as a convex program in the probabilities of the additive random vector. Once we have the optimal distribution, we propose an algorithm to generate pseudorandom realizations from this distribution using trajectories of a chaotic oscillator. At the other end of the channel, we have a second chaotic oscillator, which we use to generate realizations from the same distribution. Note that if we obtain the same realizations on both sides of the channel, we can simply subtract the realization from the distorted query to recover the requested query. To generate equal realizations, we need the two chaotic oscillators to be synchronized, i.e., we need them to generate exactly the same trajectories on both sides of the channel synchronously in time. We force the two chaotic oscillators into exponential synchronization using a driving signal. Exponential synchronization implies that trajectories of the oscillators converge to each other exponentially fast for all admissible initial conditions and are perfectly synchronized in the limit only. Thus, in finite time, there is always a “small” difference between their trajectories. To implement our algorithm, we assume (as it is often done in related work) that systems have been operating for sufficiently long time so that this small difference is negligible and oscillators are practically synchronized. We quantify the worst-case distortion induced by assuming perfect synchronization, and show that this distortion vanishes exponentially fast. Simulations are presented to illustrate our results.
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ItemOrdinal Optimisation for the Gaussian Copula Model( 2019-11-05)We present results on the estimation and evaluation of success probabilities for ordinal optimisation over uncountable sets (such as subsets of R d ). Our formulation invokes an assumption of a Gaussian copula model, and we show that the success probability can be equivalently computed by assuming a special case of additive noise. We formally prove a lower bound on the success probability under the Gaussian copula model, and numerical experiments demonstrate that the lower bound yields a reasonable approximation to the actual success probability. Lastly, we showcase the utility of our results by guaranteeing high success probabilities with ordinal optimisation.