Publications
197 results found
Neuenhofen M, Kerrigan E, 2020, A modified augmented lagrangian method for problems with inconsistentconstraints, Publisher: arXiv
We present a numerical method for the minimization of objectives that areaugmented with linear inequality constraints and large quadratic penalties ofover-determined inconsistent equality constraints. Such objectives arise fromquadratic integral penalty methods for the direct transcription of optimalcontrol problems. The Augmented Lagrangian Method (ALM) has a number of advantages over theQuadratic Penalty Method (QPM) for solving this class of problems. However, ifthe equality constraints are inconsistent, then ALM might not converge to apoint that minimizes the %unconstrained bias of the objective and penalty term.Therefore, in this paper we show a modification of ALM that fits our purpose. We prove convergence of the modified method and prove under local uniquenessassumptions that the local rate of convergence of the modified method ingeneral exceeds the one of the unmodified method. Numerical experiments demonstrate that the modified ALM can minimize certainquadratic penalty-augmented functions faster than QPM, whereas the unmodifiedALM converges to a minimizer of a significantly different problem.
Nie Y, Kerrigan EC, 2020, Solving dynamic optimization problems to a specified accuracy: an alternating approach using integrated residuals, Publisher: arXiv
We propose a novel direct transcription and solution method for solvingnonlinear, continuous-time dynamic optimization problems. Instead of forcingthe dynamic constraints to be satisfied only at a selected number of points asin direct collocation, the new approach alternates between minimizing andconstraining the squared norm of the dynamic constraint residuals integratedalong the whole solution trajectories. As a result, the method can 1) obtainsolutions of higher accuracy for the same mesh compared to direct collocationmethods, 2) enables a flexible trade-off between solution accuracy andoptimality, 3) provides reliable solutions for challenging problems, includingthose with singular arcs and high-index differential algebraic equations.
Solis-Lemus JA, Costar E, Doorly D, et al., 2020, A simulated single ventilator/dual patient ventilation strategy for acute respiratory distress syndrome during the COVID-19 pandemic, Royal Society Open Science, Vol: 7, Pages: 1-12, ISSN: 2054-5703
The potential for acute shortages of ventilators at the peak of the COVID-19 pandemic has raised the possibility of needing to support two patients from a single ventilator. To provide a system for understanding and prototyping designs, we have developed a mathematical model of two patients supported by a mechanical ventilator. We propose a standard set-up where we simulate the introduction of T-splitters to supply air to two patients and a modified set-up where we introduce a variable resistance in each inhalation pathway and one-way valves in each exhalation pathway. Using the standard set-up, we demonstrate that ventilating two patients with mismatched lung compliances from a single ventilator will lead to clinically significant reductions in tidal volume in the patient with the lowest respiratory compliance. Using the modified set-up, we demonstrate that it could be possible to achieve the same tidal volumes in two patients with mismatched lung compliances, and we show that the tidal volume of one patient can be manipulated independently of the other. The results indicate that, with appropriate modifications, two patients could be supported from a single ventilator with independent control of tidal volumes.
Faqir OJ, Kerrigan EC, Gunduz D, 2020, Information transmission bounds between moving terminals, IEEE Communications Letters, Vol: 24, Pages: 1410-1413, ISSN: 1089-7798
In networks of mobile autonomous agents, e.g. for data acquisition, we may wish to maximize data transfer or to reliably transfer a minimum amount of data, subject to quality of service or energy constraints. These requirements can be guaranteed through both offline node design/specifications and online trajectory/communications design. Regardless of the distance between them, for a stationary point-to-point transmitter-receiver pair communicating across a single link under average power constraints, the total data transfer is unbounded as time tends to infinity. In contrast, we show that if the transmitter/receiver is moving at any constant speed away from each other, then the maximum transmittable data is bounded. Although general closed-form expressions as a function of communication and mobility profile parameters do not yet exist, we provide closed-form expressions for particular cases, such as ideal free space path loss. Under more general scenarios we instead give lower bounds on the total transmittable information across a single link between mobile nodes.
Atam E, Kerrigan EC, 2020, Optimal partitioning of multi-thermal zone buildings for decentralized control, Publisher: arXiv
In this paper, we develop an optimization-based systematic approach for thechallenging, less studied, and important problem of optimal partitioning ofmulti-thermal zone buildings for the decentralized control. The proposed methodconsists of (i) construction of a graph-based network to quantitativelycharacterize the thermal interaction level between neighbor zones, and (ii) theapplication of two different approaches for optimal clustering of the resultingnetwork graph: stochastic optimization and robust optimization. The proposedmethod was tested on two case studies: a 5-zone building (a small-scaleexample) which allows one to consider all possible partitions to assess thesuccess rate of the developed method; and a 20-zone building (a large-scaleexample) for which the developed method was used to predict the optimalpartitioning of the thermal zones. Compared to the existing literature, ourapproach provides a systematic and potentially optimal solution for theconsidered problem.
Brown J, Su D, Kong H, et al., 2020, Improved noise covariance estimation in visual servoing using an autocovariance least-squares approach, Mechatronics, Vol: 68, ISSN: 0957-4158
Position based visual servoing is a widely adopted tool in robotics and automation. While the extended Kalman filter (EKF) has been proposed as an effective technique for this, it requires accurate noise covariance matrices to render desirable performance. Although numerous techniques for updating or estimating the covariance matrices have been developed in the literature, many of these suffer from computational limits or difficulties in imposing structural constraints such as positive semi-definiteness (PSD). In this paper, a relatively new framework, namely the autocovariance least-squares (ALS) method, is applied to estimate noise covariances using real world visual servoing data. To generate the innovations data required for the ALS method, we utilize standard position based visual servoing methods such as EKF, and also an advanced optimization-based framework, namely moving horizon estimation (MHE). A major advantage of the proposed method is that the PSD and other structural constraints on the noise covariances can be enforced conveniently in the optimization problem, which can be solved efficiently using existing software packages. Our results show that using the ALS estimated covariances in the EKF, instead of hand-tuned covariances, gives more than 20% mean error reduction in visual servoing, while utilising MHE to generate the ALS innovations provides a further 21% accuracy improvement.
McInerney I, Kerrigan E, Constantinides G, 2020, Modeling round-off error in the fast gradient method for predictive control, 2019 IEEE 58th Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 1-6
We present a method for determining the smallest precision required to have algorithmic stability of an implementation of the Fast Gradient Method (FGM) when solving a linear Model Predictive Control (MPC) problem in fixed-point arithmetic. We derive two models for the round-off error present in fixed-point arithmetic. The first is a generic model with no assumptions on the predicted system or weight matrices. The second is a parametric model that exploits the Toeplitz structure of the MPC problem for a Schur-stable system. We also propose a metric for measuring the amount of round-off error the FGM iteration can tolerate before becoming unstable. This metric is combined with the round-off error models to compute the minimum number of fractional bits needed for the fixed-point data type. Using these models, we show that exploiting the MPC problem structure nearly halves the number of fractional bits needed to implement an example problem. We show that this results in significant decreases in resource usage, computational energy and execution time for an implementation on a Field Programmable Gate Array.
McInerney I, Kerrigan E, Constantinides G, 2020, Closed-form preconditioner design for linear predictive control, 21st IFAC World Congress, Publisher: IFAC Secretariat, Pages: 1-4, ISSN: 2405-8963
Model Predictive Control (MPC) with linear models and constraints is extensivelybeing utilized in many applications, many of which have low power requirements and limitedcomputational resources. In these resource-constrained environments, many designers chooseto utilize simple iterative first-order optimization solvers, such as the Fast Gradient Method.Unfortunately, the convergence rate of these solvers is affected by the conditioning of the problemdata, with ill-conditioned problems requiring a large number of iterations to solve. In order toreduce the number of solver iterations required, we present a simple closed-form method forcomputing an optimal preconditioning matrix for the Hessian of the condensed primal problem.To accomplish this, we also derive spectral bounds for the Hessian in terms of the transferfunction of the predicted system. This preconditioner is based on the Toeplitz structure of theHessian and has equivalent performance to a state-of-the-art optimal preconditioner, withouthaving to solve a semidefinite program during the design phase.
Nie Y, Kerrigan EC, 2020, External constraint handling for solving optimal control problems with simultaneous approaches and interior point methods, IEEE Control Systems Letters, Vol: 4, Pages: 7-12, ISSN: 2475-1456
Inactive constraints do not contribute to the solution but increase theproblem size and burden the numerical computations. We present a novel strategyfor handling inactive constraints efficiently by systematically removing theinactive constraints and redundant constraint sets under a mesh refinementframework. The method is tailored for interior point-based solvers, which areknown to be very sensitive to the choice of initial points in terms offeasibility. In the example problem shown, the proposed scheme achieves morethan 40% reduction in computation time.
Nie Y, Kerrigan E, 2020, Efficient and more accurate representation of solution trajectories in numerical optimal control, IEEE Control Systems Letters, Vol: 4, Pages: 61-66, ISSN: 2475-1456
We show via examples that, when solving optimal control problems, representing the optimal state and input trajectory directly using interpolation schemes may not be the best choice. Due to the lack of considerations for solution trajectories in-between collocation points, large errors may occur, posing risks if this solution is to be applied. A novel solution representation method is proposed, capable of yielding a solution of much higher accuracy for the same discretization mesh. This is achieved by minimizing the integral of the residual error for the overall trajectory, instead of forcing the errors to be zero only at collocation points. In this way, the requirement for mesh resolution can be significantly reduced, leaving the problem dimensions relatively small. This particular formulation also avoids some of the drawbacks found in the earlier work of integrated residual minimization, leading to more efficient computations.
Iftikhar S, Faqir O, Kerrigan E, 2019, Nonlinear model predictive control of an overhead laboratory-scale gantry crane with obstacle avoidance, 2019 IEEE Conference on Control Technology and Applications (CCTA), Publisher: IEEE
Gantry cranes are complex nonlinear electrome- chanical systems representing a challenging control problem. We propose an optimization-based controller for guiding the crane through arbitrary obstacles. Solving path planning problems with obstacles typically requires a two-stage approach. First, a path is found that is feasible w.r.t. system dynamics and obstacles. The path is then interpreted as a series of set points by a lower-level controller that guides the system. We instead generate a path, and the associated control input to move along that path, from a single optimization problem using a nonlinear model predictive control framework. In doing so, we generate a trajectory that is locally optimal and feasible w.r.t. system dynamics and obstacles. Multiple obstacle avoidance constraint formulations are proposed as smooth, differentiable functions. Objects are approximated either as the union of a set of smooth shapes or as smooth indicator functions. The formulations presented in this work are applicable to (non-)convex problems in 2-D or 3-D spaces. Numerical methods are used to solve the proposed problems for both 2-D (fixed string length) and 3-D (varying string length) models of the gantry crane, resulting in consistently lower costs than nodal or sampling based algorithms.
Brown J, Su D, Kong H, et al., 2019, Improved noise covariance estimation in visual servoing using an autocovariance least-squares approach, Joint 12th IFAC Conference on Control Applications in Marine Systems, Robotics, and Vehicles 1st IFAC Workshop on Robot Control, Publisher: Elsevier, Pages: 37-42, ISSN: 2405-8963
For pose estimation in visual servoing, by assuming the relative motion over one sample period to be constant, many existing works adopt a linear time invariant (LTI) dynamic model. Since the standard feature point transformation is nonlinear, extended Kalman filtering (EKF) has become popular due to its simplicity. Thus, the problem at hand becomes filtering of an LTI system with a time-varying output matrix. To obtain satisfactory performance, accurate knowledge of the noise covariances is essential. Various methods have been proposed on how to adaptively update their values to improve performance. However, these techniques cannot guarantee the positive semidefiniteness (PSD) of the covariance estimates. In this paper, we propose to apply the autocovariance least-squares (ALS) approach to covariance identification in pose estimation. The ALS approach can provide reliable estimates of the covariance matrices while maintaining their PSD and imposing desired structural constraints. Our tests show that using the covariance estimates from the ALS method in EKF can reduce the average pose estimation error by more than 30% in simulation, and the average position estimation error by about 30% using experimental data, respectively, compared to a hand-tuned EKF.
Zhang L, Kerrigan E, Pal B, 2019, Optimal communication scheduling in the smart grid, IEEE Transactions on Industrial Informatics, Vol: 15, Pages: 5257-5265, ISSN: 1551-3203
This paper focuses on obtaining the optimal communication topology in the smart grid architecture, i.e., what is the optimal communication setup of smart meters in a smart building. The fact that smart meters also consume energy, more often than not, gets ignored by researchers and engineers. In this paper, we will show that smart meter networks can consume significantly less energy with optimal scheduling. Numerical results show that the overall energy consumption can be reduced by implementing the optimal communication architecture and transmission rate setup, rather than implementing a straightforward communication architecture with uniform channel bandwidth.
McInerney I, Kerrigan EC, Constantinides GA, 2019, Bounding computational complexity under cost function scaling in predictive control, Publisher: arXiv
We present a framework for upper bounding the number of iterations requiredby first-order optimization algorithms implementing constrained LQRcontrollers. We derive new bounds for the condition number and extremaleigenvalues of the primal and dual Hessian matrices when the cost function isscaled. These bounds are horizon-independent, allowing for their use withreceding, variable and decreasing horizon controllers. We considerably relaxprior assumptions on the structure of the weight matrices and assume only thatthe system is Schur-stable and the primal Hessian of the quadratic program (QP)is positive-definite. Our analysis uses the Toeplitz structure of the QPmatrices to relate their spectrum to the transfer function of the system,allowing for the use of system-theoretic techniques to compute the bounds.Using these bounds, we can compute the effect on the computational complexityof trading off the input energy used against the state deviation. An examplesystem shows a three-times increase in algorithm iterations between the twoextremes, with the state 2-norm decreased by only 5% despite a greatlyincreased state deviation penalty.
Faqir O, Nie Y, Kerrigan E, et al., 2018, Energy-efficient communication in mobile aerial relay-assisted networks using predictive control, 6th IFAC Conference on Nonlinear Model Predictive Control, Publisher: Elsevier, Pages: 197-202, ISSN: 2405-8963
Energy-efficient communication in wireless networks of mobile autonomous agents mandates joint optimization of both transmission and propulsion energy. In Faqir et al. (2017) we developed communication-theoretic data transmission and Newtonian flight mechanics models to formulate a nonlinear optimal control problem. Here we extend the previous work by generalizing the communication model to include UAV-appropriate slow fading channels and specifically investigate the potential from joint optimization of mobility and communication over a multiple access channel. Numerical results exemplify the potential energy savings available to all nodes through this joint optimization. Finally, using the slow fading channel problem formulation, we generate a chance-constrained nonlinear model predictive control scheme for control of a terrestrial network served by a single UAV relay. Closed-loop simulations are performed subject to uncertainties in both transmission and mobility models.
Nie Y, Kerrigan EC, 2018, How should rate constraints be implemented in nonlinear optimal control solvers?, 6th IFAC Conference on Nonlinear Model Predictive Control, Publisher: IFAC Secretariat, Pages: 362-367, ISSN: 2405-8963
This paper investigates the problem of implementing rate constraints when solvingnonlinear optimal control problems with direct transcription methods. We generalize theapproach of directly implementing rate constraints on the discretization mesh to all typesof collocation methods (h,pandhp), for both state and input variables. This “on mesh”implementation replaces the additional dynamic equations and nonlinear path constraints inclassical implementations with linear equations. Thus, there is no contribution to the Hessianand the contribution to the Jacobian can be precomputed, enabling faster iterations. Throughan example, the benefits of the proposed approach are demonstrated, both in terms of obtainingsingular arc-free solutions, as well as reductions in computation time of more than 20%.
Faqir OJ, Kerrigan EC, Gunduz D, 2018, Information transmission bounds in mobile communication networks, UKACC 12th International Conference on Control (CONTROL), Publisher: IEEE, Pages: 99-99
Faqir OJ, Kerrigan EC, Gunduz D, 2018, Energy-optimal control in mobile aerial relay-assisted networks, UKACC 12th International Conference on Control (CONTROL), Publisher: IEEE, Pages: 100-100
Neuenhofen MP, Kerrigan EC, 2018, Dynamic optimization with convergence guarantees, Publisher: arXiv
We present a novel direct transcription method to solve optimization problemssubject to nonlinear differential and inequality constraints. In order toprovide numerical convergence guarantees, it is sufficient for the functionsthat define the problem to satisfy boundedness and Lipschitz conditions. Ourassumptions are the most general to date; we do not require uniqueness,differentiability or constraint qualifications to hold and we avoid the use ofLagrange multipliers. Our approach differs fundamentally from state-of-the-artmethods based on collocation. We follow a least-squares approach to findingapproximate solutions to the differential equations. The objective is augmentedwith the integral of a quadratic penalty on the differential equation residualand a logarithmic barrier for the inequality constraints, as well as aquadratic penalty on the point constraint residual. The resulting unconstrainedinfinite-dimensional optimization problem is discretized using finite elements,while integrals are replaced by quadrature approximations if they cannot beevaluated analytically. Order of convergence results are derived, even ifcomponents of solutions are discontinuous.
Nie Y, Kerrigan EC, 2018, Efficient Implementation of Rate Constraints for Nonlinear Optimal Control, 2018 UKACC 12th International Conference on Control (CONTROL), Publisher: IEEE
Khusainov B, Kerrigan EC, Suardi A, et al., 2018, Nonlinear predictive control on a heterogeneous computing platform, Control Engineering Practice, Vol: 78, Pages: 105-115, ISSN: 0967-0661
We propose an implementation of an interior-point-based nonlinear predictive controller on a heterogeneous processor. The workload can be split between a general-purpose CPU and a field-programmable gate array to trade off the contradicting design objectives of control performance and computational resource usage. A new way of exploiting the structure of the KKT matrix yields significant memory savings. We report an 18x memory saving, compared to existing approaches, and a 6x speedup over a software implementation with an ARM Cortex-A9 processor. We also introduce a new release of Protoip, which abstracts low-level details of heterogeneous programming and allows processor-in-the-loop verification.
McInerney I, Kerrigan EC, 2018, Automated project-based assessment in a predictive control course, UKACC 12th International Conference on Control (CONTROL), Publisher: IEEE, Pages: 443-443
Written assessments, such as book problems and exams, have customarily been used in control courses to measure student progress, but usually only gauge their knowledge of the theoretical concepts. More complicated control methods, such as predictive control, benefit from gauging student progress through implementation projects. We present a set of automatically marked project-based assessments that test student knowledge on concepts ranging from the derivation of physics models to the creation of a closed-loop predictive controller. We present a simulation framework that allows for the students to utilize any predictive control concepts that they decide to use in their implementation. The framework then automatically tests the student solutions against multiple constraint sets and conditions to provide quantitative data for marking the assessment.
McInerney I, Constantinides G, Kerrigan EC, 2018, A Survey of the implementation of linear model predictive control on FPGAs, 6th IFAC Conference on Nonlinear Model Predictive Control, Publisher: IFAC Secretariat, Pages: 381-387, ISSN: 2405-8963
Over the past 20 years, great strides have been made in the real-time implementationof linear MPC on FPGA devices. Starting from initial work, which demonstrated the benefits ofembedding linear MPC onto FPGAs, recent work has shown sampling rates of more than 1 MHzare possible with FPGA-based implementations. This work surveys FPGA implementationsof linear MPC, with a focus on the computational architecture. This includes the choice ofnumber representation, the parallelizations exploited and the memory architecture. We discussthe transferability of those design choices to the FPGA implementation of nonlinear MPC, andprovide some future research directions related to the implementation of MPC on FPGAs.
Khusainov B, Kerrigan EC, Constantinides G, 2018, Automatic software and computing hardware co-design for predictive control, IEEE Transactions on Control Systems Technology, Vol: 27, Pages: 2295-2304, ISSN: 1063-6536
Model predictive control (MPC) is a computationally demanding control technique that allows dealing with multiple-input and multiple-output systems while handling constraints in a systematic way. The necessity of solving an optimization problem at every sampling instant often 1) limits the application scope to slow dynamical systems and/or 2) results in expensive computational hardware implementations. Traditional MPC design is based on the manual tuning of software and computational hardware design parameters, which leads to suboptimal implementations. This brief proposes a framework for automating the MPC software and computational hardware codesign while achieving an optimal tradeoff between computational resource usage and controller performance. The proposed approach is based on using a biobjective optimization algorithm, namely BiMADS. Two test studies are considered: a central processing unit and field-programmable gate array implementations of fast gradient-based MPC. Numerical experiments show that the optimization-based design outperforms Latin hypercube sampling, a statistical sampling-based design exploration technique.
Nie Y, Faqir O, Kerrigan EC, 2018, ICLOCS2: Solve your optimal control problems with less pain, 6th IFAC Conference on Nonlinear Model Predictive Control, Publisher: IFAC Secretariat, ISSN: 2405-8963
ICLOCS2 is the new version of ICLOCS (pronounced `eye-clocks') and is a comprehensive software suite for solving nonlinear optimal control problems (OCPs) in Matlab and Simulink. The toolbox builds on a wide selection of numerical methods and automated tools to assist the design and implementation of OCPs. The aim is to reduce the requirements on the experience of the user, by providing a first port of call to solve a variety of OCPs. ICLOCS2 may not be the fastest solver for some problems, but it might work where other solvers fail.
Vemuri H, Bosworth R, Morrison JF, et al., 2018, Real-time feedback control of 3D Tollmien-Schlichting waves using a dual-slot actuator geometry, Physical Review Fluids, Vol: 3, ISSN: 2469-990X
The growth of Tollmien-Schlichting (TS) waves is experimentally attenuated using a single-inputand single-output (SISO) feedback system, where the TS wave packet is generated by a surfacepoint source in a flat-plate boundary layer. The SISO system consists of a single wall-mountedhot wire as the sensor and a miniature speaker as the actuator. The actuation is achieved througha dual-slot geometry to minimise the cavity near-field effects on the sensor. The experimentalset-up to generate TS waves or wave packets is very similar to that used by Li and Gaster [1]. Theaim is to investigate the performance of the SISO control system in attenuating single-frequency,two-dimensional disturbances generated by these configurations. The necessary plant models areobtained using system identification, the controllers are then designed based on the models andimplemented in real-time to test their performance. Cancellation of the rms streamwise velocityfluctuation of TS waves is evident over a significant domain.
Thammawichai M, Baliyarasimhuni SP, Kerrigan EC, et al., 2018, Optimizing communication and computation for multi-UAV information gathering applications, IEEE Transactions on Aerospace and Electronic Systems, Vol: 54, Pages: 601-615, ISSN: 0018-9251
Typical mobile agent networks, such as multi-unmanned aerial vehicle (UAV) systems, are constrained by limited resources: energy, computing power, memory and communication bandwidth. In particular, limited energy affects system performance directly, such as system lifetime. Moreover, it has been demonstrated experimentally in the wireless sensor network literature that the total energy consumption is often dominated by the communication cost, i.e., the computational and the sensing energy are small compared to the communication energy consumption. For this reason, the lifetime of the network can be extended significantly by minimizing the communication distance as well as the amount of communication data, at the expense of increasing computational cost. In this paper, we aim at attaining an optimal tradeoff between the communication and the computational energy. Specifically, we propose a mixed-integer optimization formulation for a multihop hierarchical clustering-based self-organizing UAV network incorporating data aggregation, to obtain an energy-efficient information routing scheme. The proposed framework is tested on two applications, namely target tracking and area mapping. Based on simulation results, our method can significantly save energy compared to a baseline strategy, where there is no data aggregation and clustering scheme.
Faqir O, Kerrigan EC, Gunduz D, 2018, Joint optimization of transmission and propulsion in aerial communication networks, IEEE Conference on Decision and Control, Publisher: IEEE
Communication energy in a wireless network of mobile autonomous agents should be considered as the sum of transmission energy and propulsion energy used to facilitate the transfer of information. Accordingly, communication-theoretic and Newtonian dynamic models are developed to model the communication and locomotion expenditures of each node. These are subsequently used to formulate a novel nonlinear optimal control problem (OCP) over a network of autonomous nodes. It is then shown that, under certain conditions, the OCP can be transformed into an equivalent convex form. Numerical results for a single link between a node and access point allow for comparison with known solutions before the framework is applied to a multiple-node UAV network, for which previous results are not readily extended. Simulations show that transmission energy can be of the same order of magnitude as propulsion energy allowing for possible savings, whilst also exemplifying how speed adaptations together with power control may increase the network throughput.
Nie Y, Faqir O, Kerrigan EC, 2018, ICLOCS2: Try this optimal control problem solver before you try the rest, UKACC 12th International Conference on Control (CONTROL), Publisher: IEEE, Pages: 336-336
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Nie Y, Kerrigan EC, 2018, Capturing Discontinuities in Optimal Control Problems, UKACC 12th International Conference on Control (CONTROL), Publisher: IEEE, Pages: 338-338
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