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Journal articleScarciotti G, Astolfi A, 2017,
Data-driven model reduction by moment matching for linear and nonlinear systems
, Automatica, Vol: 79, Pages: 340-351, ISSN: 0005-1098Theory and methods to obtain reduced order models by moment matching from input/output data are presented. Algorithms for the estimation of the moments of linear and nonlinear systems are proposed. The estimates are exploited to construct families of reduced order models. These models asymptotically match the moments of the unknown system to be reduced. Conditions to enforce additional properties, e.g. matching with prescribed eigenvalues, upon the reduced order model are provided and discussed. The computational complexity of the algorithms is analyzed and their use is illustrated by two examples: we compute converging reduced order models for a linear system describing the model of a building and we provide, exploiting an approximation of the moment, a nonlinear planar reduced order model for a nonlinear DC-to-DC converter.
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Journal articlePrieto-Araujo E, Junyent-Ferre A, Clariana-Colet G, et al., 2017,
Control of Modular Multilevel Converters Under Singular Unbalanced Voltage Conditions With Equal Positive and Negative Sequence Components
, IEEE Transactions on Power Systems, Vol: 32, Pages: 2131-2141, ISSN: 0885-8950 -
Journal articleJiang J, Astolfi A, 2017,
Shared-control for a rear-wheel drive car: dynamic environments and disturbance rejection
, IEEE Transactions on Human-Machine Systems, Vol: 47, Pages: 723-734, ISSN: 2168-2291This paper studies the shared-control problem for the kinematic model of a group of rear-wheel drive cars in a (possibly) dynamic (i.e., time-varying) environment. The design of the shared-controller is based on measurements of distances to obstacles, angle differences, and the human input. The shared-controller is used to guarantee the safety of the car when the driver behaves “dangerously.” Formal properties of the closed-loop system with the shared-controller are presented through a Lyapunov-like analysis. In addition, we consider uncertainties in the dynamics and prove that the shared-controller is able to help the driver drive the car safely even in the presence of disturbances. Finally, the effectiveness of the controller is verified by two case studies: traffic at a junction and at a roundabout.
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Conference paperAngeli D, Athanasopoulos N, Jungers RM, et al., 2017,
Path-complete graphs and common Lyapunov functions
, HSCC '17, Publisher: ACM, Pages: 81-90A Path-Complete Lyapunov Function is an algebraic criterion composed of a finite number of functions, called pieces, and a directed, labeled graph defining Lyapunov inequalities between these pieces. It provides a stability certificate for discrete-time arbitrary switching systems. In this paper, we prove that the satisfiability of such a criterion implies the existence of a Common Lyapunov Function, expressed as the composition of minima and maxima of the pieces of the Path-Complete Lyapunov function. the converse however is not true even for discrete-time linear systems: we present such a system where a max-of-2 quadratics Lyapunov function exists while no corresponding Path-Complete Lyapunov function with 2 quadratic pieces exists. In light of this, we investigate when it is possible to decide if a Path- Complete Lyapunov function is less conservative than another. By analyzing the combinatorial and algebraic structure of the graph and the pieces respectively, we provide simple tools to decide when the existence of such a Lyapunov function implies that of another.
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Journal articleAnagnostou G, Pal BC, 2017,
Derivative-free Kalman filtering based approaches to dynamic state estimation for power systems with unknown inputs
, IEEE Transactions on Power Systems, Vol: 33, Pages: 116-130, ISSN: 1558-0679This paper proposes a decentralized derivative-freedynamic state estimation method in the context of a power systemwith unknown inputs, to address cases when system linearisationis cumbersome or impossible. The suggested algorithm tacklessituations when several inputs, such as the excitation voltage,are characterized by uncertainty in terms of their status. Thetechnique engages one generation unit only and its associatedmeasurements, and it remains totally independent of other systemwide measurements and parameters, facilitating in this way theapplicability of this process on a decentralized basis. The robust-ness of the method is validated against different contingencies.The impact of parameter errors, process and measurement noiseon the unknown input estimation performance is discussed. Thisunderstanding is further supported through detailed studies in arealistic power system model.
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Journal articleNanchian S, Majumdar A, Pal BC, 2017,
Ordinal optimization technique for three phase distribution network state estimation including discrete variables
, IEEE Transactions on Sustainable Energy, Vol: 8, Pages: 1528-1535, ISSN: 1949-3037This paper has discussed transformer tap position estimation with continuous and discrete variables in the context of three phase distribution state estimation (SE). Ordinal optimization (OO) technique has been applied to estimate the transformer tap position for the first time in unbalanced three phase distribution network model. The results on 129 bus system model have demonstrated that OO method can generate a reliable estimate for transformer exact tap position with discrete variables in distribution system state estimation (DSSE) and also in short period of time. In this paper the node voltages and power losses are calculated for 129 bus network. It is also demonstrated that OO is much faster than other accurate methods such HPSO. The losses obtained with OO are much accurate. In view of this OO performs better than WLS as it provides higher accuracy of the loss calculation. In a distribution network where about 5-6% of electricity generated is lost, accurate estimation of this loss has significant technical and commercial value. The authors believe the technique proposed will help realize those benefits.
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Conference paperMoreira R, Ollagnier L, Papadaskalopoulos D, et al., 2017,
Optimal Multi-Service Business Models for Electric Vehicles
, PowerTech 2017 -
Conference paperFong G, Moreira R, Strbac G, 2017,
Economic analysis of energy storage business models
, 12th IEEE Power and Energy Society PowerTech Conference 2017, Publisher: IEEEThe increasingpenetration of renewable energy systems andtheelectrification of heat and transport sectors inthe UKhave created business opportunities for flexible technologies, such as battery energy storage (BES). However,BESinvestments arestill not well understood due to a wide range and debatable technology costs that may undermine itsbusiness case. In this context, aneconomic analysis will be established to assess the economic viability ofcurrent BESbusiness models, particularly associated with multiple service portfolios. Our model quantifies the net present values (NPVs) and payback periods of BES investments considering various business models and state-of-the-art BES technologies. We determine thecommercial viability associated with different BES technologies and business models. The developed model comparesdifferent technology costs, business models(i.e. portfolio ofservicesprovided)and BES lifetimes to perform a comprehensive economic analysis on the business case for investing in BES. Several case studies under current GBmarket arrangements demonstrate that BES investment associated with multi-service business modelsoffers the best financial benefits to storage investors and achieve payback periods within 10 years’ lifetime.
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Journal articleScarciotti G, 2017,
Steady-state matching and model reduction for systems of differential-algebraic equations
, IEEE Transactions on Automatic Control, Vol: 62, Pages: 5372-5379, ISSN: 1558-2523The problem of model reduction for nonlinear differential-algebraic systems is addressed using the notions of moment and of steady-state response. These notions are formally introduced for this class of systems and families of nonlinear differential-algebraic reduced order models achieving moment matching with additional properties are presented. Stronger results for the special class of linear singular systems are provided. Two simple examples illustrate the proposed technique.
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Conference paperMoreira R, Strbac G, Papadopoulos P, et al., 2017,
Business Case in Support for Reactive Power Services from Distributed Energy Storage
, CIRED 2017 -
Book chapterScarciotti G, Astolfi A, 2017,
A Review on Model Reduction by Moment Matching for Nonlinear Systems
, Feedback Stabilization of Controlled Dynamical Systems, Editors: Petit, Publisher: Springer International Publishing, Pages: 29-52 -
Conference paperAldhaher S, Mitcheson PD, Arteaga JM, et al., 2017,
Light-Weight Wireless Power Transfer for Mid-Air Charging of Drones
, 11th European Conference on Antennas and Propagation (EUCAP), Publisher: IEEE, Pages: 336-340, ISSN: 2164-3342 -
Journal articleCai L, Thornhill NF, Kuenzel S, et al., 2017,
Real-time detection of power system disturbances based on k-nearest neighbor analysis
, IEEE Access, Vol: 5, Pages: 5631-5639, ISSN: 2169-3536Efficient disturbance detection is important for power system security and stability. In this paper, a new detection method is proposed based on a time series analysis technique known as k nearest neighbor (kNN) analysis. Advantages of this method are that it can deal with the electrical measurements with oscillatory trends and can be implemented in real time. The method consists of two stages which are the off-line modelling and the on-line detection. The off-line stage calculates a sequence of anomaly index values using kNN on the historical ambient data and then determines the detection threshold. Afterwards, the on-line stage calculates the anomaly index value of presently measured data by readopting kNN and compares it with the established threshold for detecting disturbances. To meet the real-time requirement, strategies for recursively calculating the distance metrics of kNN and for rapidly picking out the kth smallest metric are built. Case studies conducted on simulation data from the reduced equivalent model of Great Britain power system and measurements from an actual power system in Europe demonstrate the effectiveness of the proposed method.
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Journal articleCai L, Thornhill NF, Pal BC, 2017,
Multivariate detection of power system disturbances based on fourth order moment and singular value decomposition
, IEEE Transactions on Power Systems, Vol: 32, Pages: 4289-4297, ISSN: 1558-0679This paper presents a new method to detect power system disturbances in a multivariate context, which is based on Fourth Order Moment (FOM) and multivariate analysisimplemented as Singular Value Decomposition (SVD). The motivation for this development is that power systems are increasingly affected by various disturbances and there is a requirement for the analysis of measurements to detect these disturbances. The application results on the measurements of an actual power system in Europe illustrate that the proposed multivariate detection method achieves enhanced detection reliability and sensitivity.
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Journal articleZhang X, Xiang X, Green TC, et al., 2017,
Operation and performance of resonant modular multilevel converter with flexible step ratio
, IEEE Transactions on Industrial Electronics and Control Instrumentation, Vol: 64, Pages: 6276-6286, ISSN: 0018-9421Resonant modular multilevel converters (RMMCs)have been proposed for high voltage dc-dc applications. Using dif-ferent modulation strategies, RMMC operates in different modesand achieves flexible step ratio. To provide a comprehensive studyof RMMCs, this paper presents the modulation method achievinga wide range of step ratio with the ability of inherent-balancing.The conditions for guaranteeing the inherent-balancing abilityare provided. The operation principle and performance of theRMMC are presented in this paper, which have been exploredin a case study. The experimental results are obtained from abench-scale setup, which have verified the theoretical analysis.
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Journal articleGe M, Kerrigan EC, 2017,
Noise covariance identification for nonlinear systems using expectation maximization and moving horizon estimation
, Automatica, Vol: 77, Pages: 336-343, ISSN: 0005-1098In order to estimate states from a noise-driven state space system, the state estimator requires a priori knowledge of both process and output noise covariances. Unfortunately, noise statistics are usually unknown and have to be determined from output measurements. Current expectation maximization (EM) based algorithms for estimating noise covariances for nonlinear systems assume the number of additive process and output noise signals are the same as the number of states and outputs, respectively. However, in some applications, the number of additive process noises could be less than the number of states. In this paper, a more general nonlinear system is considered by allowing the number of process and output noises to be smaller or equal to the number of states and outputs, respectively. In order to estimate noise covariances, a semi-definite programming solver is applied, since an analytical solution is no longer easy to obtain. The expectation step in current EM algorithms rely on state estimates from the extended Kalman filter (EKF) or smoother. However, the instability and divergence problems of the EKF could cause the EM algorithm to converge to a local optimum that is far away from true values. We use moving horizon estimation instead of the EKF/smoother so that the accuracy of the covariance estimation in nonlinear systems can be significantly improved.
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Journal articlePIpelzadeh Y, Moreno R, Chaudhuri B, et al., 2017,
Corrective control with transient assistive measures: value assessment for Great Britain transmission system
, IEEE Transactions on Power Systems, Vol: 32, Pages: 1638-1650, ISSN: 0885-8950In this paper, the efficacy and value of using corrective control supported by transient assistive measures (TAM) is quantified in terms of the cost savings due to less constrained operation of the system. The example TAM is a rapid modulation of the power order of the high-voltage direct current (HVDC) links in the system so as to improve transient stability during corrective control. A sequential approach is used for the offline value assessment: a security constrained economic dispatch (SCED) module (master problem) determines the optimal generation dispatch, HVDC settings, and the corrective control actions to be used post-fault (generation and demand curtailed) so as to minimize the operational costs while ensuring static security. The transient stability module (slave problem) assesses the dynamic stability for the operating condition set by the SCED and, if needed, applies appropriate TAM to maintain the system transiently stable. If this is not possible, the master module uses a tighter set of security constraints to update the dispatch and other settings until the system can be stabilized. A case-study on the Great Britain system is used to demonstrate that corrective control actions supported by TAM facilitate significantly higher pre-fault power transfers whilst maintaining N-2 security.
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Conference paperLi PENG, Boem F, Pin G, et al., 2017,
Distributed fault detection and isolation for interconnected systems: a non-asymptotic kernel-based approach
, 20th IFAC World Congress, Publisher: IFACIn this paper, a novel framework is proposed for deadbeat distributed Fault Detectionand Isolation (FDI) of large-scale continuous-time LTI dynamic systems. The monitoredsystem is composed of several subsystems which are linearly interconnected with unknownparameterization. Each subsystem is monitored by a local diagnoser based on the measuredlocal output, local inputs and the interconnection variables from the neighboring subsystems.The local FDI decision is based on two non-asymptotic state-parameter estimators using Volterraintegral operators which eliminate the effect of the unknown initial conditions so that theestimates converge to the true value in a deadbeat manner and therefore the fault diagnosiscan be achieved in finite time. Moreover, the unknown interconnection parameters and theunknown fault parameters are simultaneously estimated. Numerical examples are included toshow the effectiveness of the proposed FDI architecture.
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Conference paperPapadaskalopoulos, Ye Y, strbac, 2018,
Exploring the Role of Demand Shifting in Oligopolistic Electricity Markets
, 2017 IEEE Power & Energy Society General Meeting (GM), Publisher: IEEEPrevious work has demonstrated that the priceelasticity of the demand side reduces electricity producers’ability to exercise market power. However, price elasticitycannot capture alone consumers’ flexibility, as the latter mainlyinvolves shifting of loads’ operation in time. This paper providesfor the first time qualitative and quantitative analysis of thevalue of demand shifting in mitigating market power by thegeneration side. An equilibrium programming model of theoligopolistic market setting is developed, taking into account theinter-temporal characteristics of demand shifting. The decisionmaking process of each strategic producer is modelled through abi-level optimization problem, which is solved aftertransforming it to a Mathematical Program with EquilibriumConstraints (MPEC). The market equilibria resulting from theinteraction of multiple independent producers are determinedby employing an iterative diagonalization method. Case studieson a test market with day-ahead horizon and hourly resolutionquantitatively demonstrate the benefits of demand shifting inlimiting generation market power, by employing relevantindexes from the literature.
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Conference paperArteaga JM, Aldhaher S, Kkelis G, et al., 2017,
Design of a 13.56 MHz IPT system optimised for dynamic wireless charging environments
, 2nd IEEE Annual Southern Power Electronics Conference (SPEC), Publisher: IEEE, Pages: 1-6Inductive power transfer (IPT) systems are often designed to achieve their highest efficiency at a fixed load value and at a fixed coil separation distance and misalignment. A variation in the position of the coils or the load value tends to drastically affect the efficiency, and therefore makes the designed IPT system not practical for applications that are mobile with variable loading conditions such as dynamic wireless charging for electric vehicles. This paper presents a novel design approach for loosely-coupled IPT systems that can inherently maintain efficient operation against changes in the system's characteristics, coil geometries and loading conditions. The transmitting-end of the proposed IPT system consists of a Load-Independent Class EF inverter that provides a constant amplitude current in the transmitting-end coil and achieves zero-voltage switching (ZVS) independent of the coupling factor and the load resistance. A Class D rectifier with a resistance compression network (RCN) was implemented for the receiving-end of the IPT system to ensure that the reflected resistance to the transmitting-end is at its optimum value with minimal dependence on the output load resistance. The combination of the features of the inverter and rectifier allow the IPT system to operate efficiently across a wide range of air gaps, without retuning. Experimental results show a maximum DC-DC efficiency of 83% with a coil separation of one coil diameter and 85 W output power. A weighted average DC-DC energy transfer efficiency (where the coils move through zero alignment, to full alignment, and back to zero alignment at constant velocity), was measured at 73%.
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Journal articleKiviluoma J, Heinen S, Qazi H, et al., 2017,
Harnessing Flexibility from Hot and Cold
, IEEE POWER & ENERGY MAGAZINE, Vol: 15, Pages: 25-33, ISSN: 1540-7977 -
Journal articleNduka O, Pal BC, 2017,
Harmonic domain modelling of PV system for the assessment of grid integration impact
, IEEE Transactions on Sustainable Energy, Vol: 8, Pages: 1154-1165, ISSN: 1949-3037In this paper, a comprehensive harmonic domainreference frame (HDRF) model of a voltage source converter(VSC) grid interactive photovoltaic (PV) system is presented.The model is useful for assessing the harmonic coupling betweenthe PV system and the network. Different components of the PVsystem such as inverter, LCL filter and interconnecting trans-former have been incorporated in the model. Using this model,harmonic currents from PV system connected to both distortedand undistorted networks have been quantified. Also, the modelhas been deployed in investigating resonance occurrence in amedium-voltage distribution network (MVDN) where the resultsprovide interesting technical insight and understanding.
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Conference paperPicciau A, Inggs G, Wickerson J, et al., 2017,
Balancing locality and concurrency: solving sparse triangular systems on GPUs
, 23rd IEEE International Conference on High Peformance Computing, Data, and Analytics (HiPC), Publisher: IEEE, Pages: 183-192Many numerical optimisation problems rely onfast algorithms for solving sparse triangular systems of linearequations (STLs). To accelerate the solution of such equations,two types of approaches have been used: on GPUs, concurrencyhas been prioritised to the disadvantage of data locality, whileon multi-core CPUs, data locality has been prioritised to thedisadvantage of concurrency.In this paper, we discuss the interaction between data localityand concurrency in the solution of STLs on GPUs, and we presenta new algorithm that balances both. We demonstrate empiricallythat, subject to there being enough concurrency available in theinput matrix, our algorithm outperforms Nvidia’s concurrencyprioritisingCUSPARSE algorithm for GPUs. Experimental resultsshow a maximum speedup of 5.8-fold.Our solution algorithm, which we have implemented inOpenCL, requires a pre-processing phase that partitions thegraph associated with the input matrix into sub-graphs, whosedata can be stored in low-latency local memories. This preliminaryanalysis phase is expensive, but because it depends onlyon the input matrix, its cost can be amortised when solving formany different right-hand sides.
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Conference paperAunedi M, Pudjianto D, Strbac G, 2017,
Calculating system integration costs of low-carbon generation technologies in future GB electricity system
, 5th IET International Conference on Renewable Power Generation (RPG) 2016, Publisher: Institution of Engineering and TechnologySystem integration costs (SIC) of generation technologies, also referred to as system externalities, include various categories of additional costs that are incurred in the system in addition to the cost of building and operating the generation capacity that is added to the system. SIC may include increased balancing cost, cost of additional backup capacity, cost of reinforcing network infrastructure and the cost of maintaining system carbon emissions. In this paper we present a whole-system approach to quantifying the SIC and explore different approaches to calculating the relative SIC of a generation technology when compared to another technology. The results show that the SIC of low-carbon generation technologies will significantly depend on the composition of the generation mix, with higher penetrations of variable renewables giving rise to a higher SIC. Also, SIC will significantly depend on the deployment level of flexible options such as more flexible generation technologies, energy storage, demand side response or interconnection. The additional system cost driven by low-carbon technologies can provide a very useful input to inform the energy policy and support the selection of the low-carbon portfolio with the lowest total system cost.
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Journal articleTeng F, Strbac G, 2017,
Full stochastic scheduling for low-carbon electricity systems
, IEEE Transactions on Automation Science and Engineering, Vol: 14, Pages: 451-470, ISSN: 1558-3783High penetration of renewable generation will increase the requirement for both operating reserve and frequency response, due to its variability, uncertainty and limited inertia capability. Although the importance of optimal scheduling of operating reserve has been widely studied, the scheduling of frequency response has not yet been fully investigated. In this context, this paper proposes a computationally-efficient mixed integer linear programming formulation for a full stochastic scheduling model that simultaneously optimizes energy production, operating reserve, frequency response and under-frequency load shedding. By using value of lost load as the single security measure, the model optimally balances the cost associated with the provision of various ancillary services against the benefit of reduced cost of load curtailment. The proposed model is applied in a 2030 GB system to demonstrate its effectiveness. Impact of installed capacity of wind generation and setting of value of lost load are also analysed. Note to Practitioners— One of the obstacles for large scale deployment of wind generation is the challenges it imposes on the efficient operation of the electricity system. This paper presents a full stochastic scheduling model. The long-term uncertainty driven by wind forecasting errors and short-term uncertainty driven by generation outages are modelled by using scenario tree and capacity outage probability table, respectively. The model leads to significant operation cost saving within reasonable computational time. The proposed model could be applied in real large-scale power systems to support the cost-effective integration of wind generation.
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Journal articleParisini T, Pin G, Chen B, 2017,
Robust finite-time estimation of biased sinusoidal signals: a volterra operators approach
, Automatica, Vol: 77, Pages: 120-132, ISSN: 0005-1098A novel finite-time convergent estimation technique is proposed for identifying the amplitude, frequency and phase of abiasedsinusoidal signal. Resorting to Volterra integral operators with suitably designed kernels, the measured signal is processedyielding a set of auxiliary signals in which the influence of the unknown initial conditions is removed. A second-order slidingmode-based adaptation law – fed by the aforementioned auxiliary signals – is designed for finite-time estimation of the frequency,amplitude, and phase. The worst case behavior of the proposed algorithm in presence of the bounded additive disturbancesis fully characterized by Input-to-State Stability arguments. The effectiveness of the estimation technique is evaluated andcompared with other existing tools via extensive numericalsimulations.
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Journal articleManfredi S, Angeli D, 2017,
Necessary and sufficient conditions for consensus in nonlinear monotone networks with unilateral interactions
, Automatica, Vol: 77, Pages: 51-60, ISSN: 0005-1098This paper deals with an extended framework of the distributed asymptotic agreement problem by allowing the presence of unilateral interactions (optimistic or pessimistic) in place of bilateral ones, for a large class of nonlinear monotone time-varying networks. In this original setup we firstly introduce notions of unilateral optimistic and/or pessimistic interaction, of associated bicolored edge in the interaction graph and a suitable graph-theoretical connectedness property. Secondly, we formulate a new assumption of integral connectivity and show that it is sufficient to guarantee exponential convergence towards the agreement subspace. Finally, we show that the proposed conditions are also necessary for consensuability and discuss how the new notions of bicolored graph and related connectivity concepts encompass the usual criteria in the standard case of bilateral interactions. Theoretical advances are emphasized through illustrative examples given both to support the discussion and to highlight how the proposed framework extends all existing conditions for consensus of monotone networks.
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Conference paperAl-Radhawi MA, Angeli D, 2017,
Construction of robust Lyapunov functions for reaction networks
, European Control Conference (ECC), Publisher: IEEE, Pages: 928-935Although Chemical Reaction Networks (CRNs) form a rich class of nonlinear systems that can exhibit wide range of nonlinear behaviours, many common examples are observed to be asymptotically stable regardless of the kinetics. This paper presents the recently uncovered class of Graphically Stable Networks (GSNs) which is characterized by the existence of a robust Lyapunov function defined in the reaction coordinates. Subject to mild conditions, the existence of these functions guarantees asymptotic stability of a network regardless of the specific form of kinetics. Construction methods for these functions are provided and illustrated by examples.
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Conference paperZhou Y, Boem F, Fischione C, et al., 2017,
Distributed Fault Detection with Sensor Networks using Pareto-Optimal Dynamic Estimation Method
, 2016 European Control Conference, Publisher: IEEEIn this paper, a distributed method for faultdetection using sensor networks is proposed. Each sensorcommunicates only with neighboring nodes to compute locallyan estimate of the state of the system to monitor. A residualis defined and suitable stochastic thresholds are designed,allowing to set the parameters so to guarantee a maximumfalse alarms probability. The main novelty and challenge ofthe proposed approach consists in addressing the individualcorrelations between the state, the measurements, and thenoise components, thus significantly generalising the estimationmethodology compared to previous results. No assumptions onthe probability distribution family are needed for the noisevariables. Simulation results show the effectiveness of theproposed method, including an extensive sensitivity analysiswith respect to fault magnitude and measurement noise.
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Conference paperKhusainov B, Kerrigan EC, Constantinides GA, 2017,
Multi-objective Co-design for Model Predictive Control with an FPGA
, European Control Conference 16, Publisher: IEEE, Pages: 110-115In order to achieve the best possible performanceof a model predictive controller (MPC) for a given set ofresources, the software algorithm and computational platformhave to be designed simultaneously. Moreover, in practicalapplications the controller design problem has a multi-objectivenature: performance is traded off against computational hardwareresource usage, namely time, energy and space. Thispaper proposes formulating an MPC design problem as a multiobjectiveoptimization (MOO) problem in order to explore thedesign trade-offs in a systematic way.Since the design objectives in the resulting MOO problem areexpensive to evaluate, i.e. evaluation requires time consumingsimulations, most of the classical and evolutionary MOOalgorithms cannot be employed for this class of design problems.For this reason a practical MOO algorithm that can deal withexpensive-to-evaluate functions is presented. The algorithm isbased on Kriging and the hypervolume criterion that wasrecently proposed in the expensive optimization literature. Anumerical example for a fast gradient-based controller designshows that the proposed approach can efficiently exploreoptimal performance-resource trade-offs.
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