 Electrical and Electronic Engineering  Research Publications
Electrical and Electronic Engineering  Research Publications
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ItemOn Eigenvalues of Laplacian Matrix for a Class of Directed Signed GraphsAhmadizadeh, S ; Shames, I ; Martin, S ; Nesic, D ( 20170512)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 nonzero 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.

ItemSecurity Metrics of Networked Control Systems under Sensor Attacks (extended preprint)Murguia, C ; Shames, I ; Ruths, J ; Nesic, D ( 20180914)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 timeinvariant 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 attackfree system performance is guaranteed.

ItemOn Privacy of Quantized Sensor Measurements through Additive NoiseMurguia, C ; Shames, I ; Farokhi, F ; Nesic, D ( 20180910)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.

ItemInformationTheoretic Privacy through Chaos Synchronization and Optimal Additive NoiseMurguia, C ; Shames, I ; Farokhi, F ; Nesic, D ( 20190603)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 worstcase distortion induced by assuming perfect synchronization, and show that this distortion vanishes exponentially fast. Simulations are presented to illustrate our results.

ItemOrdinal Optimisation for the Gaussian Copula ModelChin, R ; Rowe, JE ; Shames, I ; Manzie, C ; Nešić, D ( 20191105)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.

ItemActive Learning for Linear ParameterVarying System IdentificationChin, R ; Maass, AI ; Ulapane, N ; Manzie, C ; Shames, I ; Nešić, D ; Rowe, JE ; Nakada, H ( 20200502)Active learning is proposed for selection of the next operating points in the design of experiments, for identifying linear parametervarying systems. We extend existing approaches found in literature to multipleinput multipleoutput 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 airpath model, and demonstrate that measures of model uncertainty can be successfully reduced using the proposed framework.

ItemTracking and regret bounds for online zerothorder Euclidean and Riemannian optimisationMaass, AI ; Manzie, C ; Nesic, D ; Manton, JH ; Shames, I ( 20201001)We study numerical optimisation algorithms that use zerothorder information to minimise timevarying geodesicallyconvex cost functions on Riemannian manifolds. In the Euclidean setting, zerothorder algorithms have received a lot of attention in both the timevarying and timeinvariant 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.

ItemA Sequential Learning Algorithm for Probabilistically Robust Controller TuningChin, R ; Manzie, C ; Shames, I ; Nešić, D ; Rowe, JE ( 20210218)We introduce a sequential learning algorithm to address a robust controller tuning problem, which in effect, finds (with high probability) a candidate solution satisfying the internal performance constraint to a chanceconstrained program which has blackbox functions. The algorithm leverages ideas from the areas of randomised algorithms and ordinal optimisation, and also draws comparisons with the scenario approach; these have all been previously applied to finding approximate solutions for difficult design problems. By exploiting statistical correlations through blackbox sampling, we formally prove that our algorithm yields a controller meeting the prescribed probabilistic performance specification. Additionally, we characterise the computational requirement of the algorithm with a probabilistic lower bound on the algorithm's stopping time. To validate our work, the algorithm is then demonstrated for tuning model predictive controllers on a diesel engine airpath across a fleet of vehicles. The algorithm successfully tuned a single controller to meet a desired tracking error performance, even in the presence of the plant uncertainty inherent across the fleet. Moreover, the algorithm was shown to exhibit a sample complexity comparable to the scenario approach.

ItemOrdinal Optimisation and the Offline Multiple Noisy Secretary ProblemChin, R ; Rowe, JE ; Shames, I ; Manzie, C ; Nešić, D ( 20210602)We study the success probability for a variant of the secretary problem, with noisy observations and multiple offline selection. Our formulation emulates, and is motivated by, problems involving noisy selection arising in the disciplines of stochastic simulation and simulationbased optimisation. In addition, we employ the philosophy of ordinal optimisation  involving an ordinal selection rule, and a percentile notion of goal softening for the success probability. As a result, it is shown that the success probability only depends on the underlying copula of the problem. Other general properties for the success probability are also presented. Specialising to the case of Gaussian copulas, we also derive an analytic lower bound for the success probability, which may then be inverted to find sufficiently large sample sizes that guarantee a high success probability arbitrarily close to one.

ItemTuning of multivariable model predictive controllersthrough expert bandit feedbackIra, AS ; Manzie, C ; Shames, I ; Chin, R ; Nesic, D ; Nakada, H ; Sano, T ( 20200209)For certain industrial control applications an explicit function capturing the nontrivial tradeoff between competing objectives in closed loop performance is not available. In such scenarios it is common practice to use the human innate ability to implicitly learn such a relationship and manually tune the corresponding controller to achieve the desirable closed loop performance. This approach has its deficiencies because of individual variations due to experience levels and preferences in the absence of an explicit calibration metric. Moreover, as the complexity of the underlying system and/or the controller increase, in the effort to achieve better performance, so does the tuning time and the associated tuning cost. To reduce the overall tuning cost, a tuning framework is proposed herein, whereby a supervised machine learning is used to extract the humanlearned cost function and an optimization algorithm that can efficiently deal with a large number of variables, is used for optimizing the extracted cost function. Given the interest in the implementation across many industrial domains and the associated high degree of freedom present in the corresponding tuning process, a Model Predictive Controller applied to air path control in a diesel engine is tuned for the purpose of demonstrating the potential of the framework.