Electrical and Electronic Engineering - Research Publications
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ItemCloseness of Solutions for Singularly Perturbed Systems via Averaging( 2018-09-20)This paper studies the behavior of singularly perturbed nonlinear differential equations with boundary-layer solutions that do not necessarily converge to an equilibrium. Using the average of the fast variable and assuming the boundary layer solutions converge to a bounded set, results on the closeness of solutions of the singularly perturbed system to the solutions of the reduced average and boundary layer systems over a finite time interval are presented. The closeness of solutions error is shown to be of order O(\sqrt(\epsilon)), where \epsilon is the perturbation parameter.
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ItemAdaptive Scan for Atomic Force Microscopy Based on Online Optimisation: Theory and Experiment( 2019-02-11)A major challenge in Atomic Force Microscopy (AFM) is to reduce the scan duration while retaining the image quality. Conventionally, the scan rate is restricted to a sufficiently small value in order to ensure a desirable image quality as well as a safe tip-sample contact force. This usually results in a conservative scan rate for samples that have a large variation in aspect ratio and/or for scan patterns that have a varying linear velocity. In this paper, an adaptive scan scheme is proposed to alleviate this problem. A scan line-based performance metric balancing both imaging speed and accuracy is proposed, and the scan rate is adapted such that the metric is optimised online in the presence of aspect ratio and/or linear velocity variations. The online optimisation is achieved using an extremum-seeking (ES) approach, and a semi-global practical asymptotic stability (SGPAS) result is shown for the overall system. Finally, the proposed scheme is demonstrated via both simulation and experiment.
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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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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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ItemModel Predictive Control for Lithium-Ion Battery Optimal Charging(IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC, 2018-04)Charging time and lifetime are important performances for lithium-ion (Li-ion) batteries, but are often competing objectives for charging operations. Model-based charging controls are challenging due to the complicated battery system structure that is composed of nonlinear partial differential equations and exhibits multiple time-scales. This paper proposes a new methodology for battery charging control enabling an optimal tradeoff between the charging time and battery state-of-health (SOH). Using recently developed model reduction approaches, a physics-based low-order battery model is first proposed and used to formulate a model-based charging strategy. The optimal fast charging problem is formulated in the framework of tracking model predictive control (MPC). This directly considers the tracking performance for provided state-of-charge and SOH references, and explicitly addresses constraints imposed on input current and battery internal state. The capability of this proposed charging strategy is demonstrated via simulations to be effective in tracking the desirable SOH trajectories. By comparing with the constant-current constant-voltage charging protocol, the MPC-based charging appears promising in terms of both the charging time and SOH. In addition, this obtained charging strategy is practical for real-time implementation.
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ItemHybrid Extremum Seeking for Black-Box Optimization in Hybrid Plants: An Analytical Framework(IEEE, 2018-01-01)This paper presents an analytical framework to design and analyze hybrid extremum seeking controllers for plants with hybrid dynamics. The extremum seeking controllers are characterized by a hybrid dither generator, a hybrid Jacobian estimator, and a hybrid dynamic optimizer. This structure allows us to consider a family of novel extremum seeking controllers that have not been studied in the literature before. Moreover, the hybrid extremum seeking controllers can be applied to plants with hybrid dynamics generating well-defined response maps. A convergence result is established for the closed -loop system by using singular perturbation theory for hybrid dynamical systems with hybrid boundary layers.
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ItemMesh adaptation in direct collocated nonlinear model predictive control(WILEY, 2018-10-01)Summary Direct methods are often deployed to solve nonlinear model predictive control problems where the optimal control problem is first transcribed into a nonlinear program and then solved to obtain the control input. This makes the computational cost of direct methods nontrivial; however, efficiencies can be gained by utilizing adaptation methods during transcription. Goal‐oriented a priori error estimation is used as an adaptation strategy. Unlike other strategies, the refinement is directly related to the cost function. Therefore, refinement only occurs where it is needed with respect to the cost function. Two examples are presented and an improvement of up to 50% in the computational time is observed with no degradation in the closed‐loop performance.
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ItemConvergence of full-order observers for the slow states of a singularly perturbed system (Part II: Applications)(IEEE Press, 2019-01-10)Many natural and engineered systems exhibit a singularly perturbed structure where different time scales inherently lead to difficulties in the design of observers for the system. In our related work [1], we have shown that, under appropriate assumptions, an observer designed for the slow part of the system can be applied and results in semi-global practical asymptotical (SPA) stability of the estimation error. In this paper, we show that assumptions from [1] hold for two classes of plants and nonlinear observers. In fact, we show that the provided framework in [1] covers current results in the literature and also other cases that are not covered by existing results. Hence, we demonstrate that we generalise existing results in the literature.
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ItemConvergence of full-order observers for the slow states of a singularly perturbed system (Part I: Theory)(IEEE Press, 2019-01-10)Estimation of physical variables of nonlinear systems with two-time scales is a hard task to address. Whilst nonlinear systems exhibiting a singularly perturbed structure are common in engineering applications, current observer design results apply only to a specific class of plants and observers. We consider a broader class of plants and observers to generalise existing results on observer design for slow states of nonlinear singularly perturbed systems. Under reasonable assumptions, it is shown that the estimation error can be made semi-globally practically asymptotically stable in the singular perturbation parameter. This subsequently leads to appropriate conditions for the observer design for slow variables that guarantee satisfactory estimation error performance in the full system.