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.
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ItemActive Learning for Linear Parameter-Varying System Identification( 2020-05-02)Active learning is proposed for selection of the next operating points in the design of experiments, for identifying linear parameter-varying systems. We extend existing approaches found in literature to multiple-input multiple-output systems with a multivariate scheduling parameter. Our approach is based on exploiting the probabilistic features of Gaussian process regression to quantify the overall model uncertainty across locally identified models. This results in a flexible framework which accommodates for various techniques to be applied for estimation of local linear models and their corresponding uncertainty. We perform active learning in application to the identification of a diesel engine air-path model, and demonstrate that measures of model uncertainty can be successfully reduced using the proposed framework.
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ItemTracking and regret bounds for online zeroth-order Euclidean and Riemannian optimisation( 2020-10-01)We study numerical optimisation algorithms that use zeroth-order information to minimise time-varying geodesically-convex cost functions on Riemannian manifolds. In the Euclidean setting, zeroth-order algorithms have received a lot of attention in both the time-varying and time-invariant cases. However, the extension to Riemannian manifolds is much less developed. We focus on Hadamard manifolds, which are a special class of Riemannian manifolds with global nonpositive curvature that offer convenient grounds for the generalisation of convexity notions. Specifically, we derive bounds on the expected instantaneous tracking error, and we provide algorithm parameter values that minimise the algorithm’s performance. Our results illustrate how the manifold geometry in terms of the sectional curvature affects these bounds. Additionally, we provide dynamic regret bounds for this online optimisation setting. To the best of our knowledge, these are the first regret bounds even for the Euclidean version of the problem. Lastly, via numerical simulations, we demonstrate the applicability of our algorithm on an online Karcher mean problem.
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ItemAsynchronous Distributed Optimization via Dual Decomposition and Block Coordinate Subgradient Methods(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2021-09-01)In this article, we study the problem of minimizing the sum of potentially nondifferentiable convex cost functions with partially overlapping dependences in an asynchronous manner, where communication in the network is not coordinated. We study the behavior of an asynchronous algorithm based on dual decomposition and block coordinate subgradient methods under assumptions weaker than those used in the literature. At the same time, we allow different agents to use local stepsizes with no global coordination. Sufficient conditions are provided for almost sure convergence to the solution of the optimization problem. Under additional assumptions, we establish a sublinear convergence rate that, in turn, can be strengthened to the linear convergence rate if the problem is strongly convex and has Lipschitz gradients. We also extend available results in the literature by allowing multiple and potentially overlapping blocks to be updated at the same time with nonuniform and potentially time-varying probabilities assigned to different blocks. A numerical example is provided to illustrate the effectiveness of the algorithm.
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ItemGaussian Processes with Monotonicity Constraints for Preference Learning from Pairwise Comparisons(IEEE, 2018)In preference learning, it is beneficial to incorporate monotonicity constraints for learning utility functions when there is prior knowledge of monotonicity. We present a novel method for learning utility functions with monotonicity constraints using Gaussian process regression. Data is provided in the form of pairwise comparisons between items. Using conditions on monotonicity for the predictive function, an algorithm is proposed which uses the weighted average between prior linear and maximum a posteriori (MAP) utility estimates. This algorithm is formally shown to guarantee monotonicity of the learned utility function in the dimensions desired. The algorithm is tested in a Monte Carlo simulation case study, in which the results suggest that the learned utility by the proposed algorithm performs better in prediction than the standalone linear estimate, and enforces monotonicity unlike the MAP estimate.
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ItemA machine learning approach for tuning model predictive controllers(IEEE, 2018-01-01)Many industrial domains are characterized by Multiple-Input-Multiple-Output (MIMO) systems for which an explicit relationship capturing the nontrivial trade-off between the competing objectives is not available. Human experts have the ability to implicitly learn such a relationship, which in turn enables them to tune the corresponding controller to achieve the desirable closed-loop performance. However, as the complexity of the MIMO system and/or the controller increase, so does the tuning time and the associated tuning cost. To reduce the tuning cost, a framework is proposed in which a machine learning method for approximating the human-learned cost function along with an optimization algorithm for optimizing it, and consequently tuning the controller, are employed. In this work the focus is on the tuning of Model Predictive Controllers (MPCs), given both the interest in their implementations across many industrial domains and the associated high degrees of freedom present in the corresponding tuning process. To demonstrate the proposed approach, simulation results for the tuning of an air path MPC controller in a diesel engine are presented.
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