179 results found
Neuenhofen M, Kerrigan E, 2022, Solving problems with inconsistent constraints with a modified augmented lagrangian method, IEEE Transactions on Automatic Control, ISSN: 0018-9286
We present a numerical method for theminimization of constrained optimization problemswhere the objective is augmented with large quadraticpenalties of inconsistent equality constraints. Such ob-jectives arise from quadratic integral penalty methodsfor the direct transcription of optimal control prob-lems. The Augmented Lagrangian Method (ALM) hasa number of advantages over the Quadratic PenaltyMethod (QPM). However, if the equality constraintsare inconsistent, then ALM might not converge to apoint that minimizes the bias of the objective andpenalty term. Therefore, we present a modification ofALM that fits our purpose. We prove convergence ofthe modified method and bound its local convergencerate by that of the unmodified method. Numericalexperiments demonstrate that the modified ALM canminimize certain quadratic penalty-augmented func-tions faster than QPM, whereas the unmodified ALMconverges to a minimizer of a significantly differentproblem.
Faqir O, Kerrigan E, 2022, Inaccuracy matters: Accounting for solution accuracy in event-triggered nonlinear model predictive control, IEEE Transactions on Automatic Control, ISSN: 0018-9286
We consider the effect of using approximate system predictions in event-triggered control schemes. These approximations often result from using numerical transcription methods for solving continuous-time optimal control problems. Mesh refinement can guarantee upper bounds on the errorin the differential equations that model the system dynamics. We employ the accuracy guarantees of a mesh refinement scheme to show that the proposed event-triggering scheme, which compares the measured system with approximate state predictions, can be used with a guaranteed strictly positive inter-update time. Furthermore, if knowledge of the employedtranscription scheme or the approximation errors are available, then better online estimates of inter-update times can be obtained. We also detail a method of tightening constraints on the approximate system trajectory to guarantee constraint satisfaction of the continuous-time system. This is the first work to incorporate prediction accuracy in triggering metrics to guarantee reliable lower bounds for inter-update times and perform solution-dependent constraint tightening.
O'Dwyer E, Falugi P, Shah N, et al., 2022, Automating the data-driven predictive control design process for building thermal management, ECOS 2022 35th International Conference on Efficiency, Cost, Optimization, Simulation and Environmental Impact of Energy Systems
McInerney I, Kerrigan EC, 2022, Teaching Predictive Control Using Specification-based Summative Assessments, 13th Symposium on Advances in Control Education, Publisher: Elsevier, ISSN: 2405-8963
Including Model Predictive Control (MPC) in the undergraduate/graduate control curriculum is becoming vitally important due to the growing adoption of MPC in many industrial areas. In this paper, we present an overview of the predictive control course taught by the authors at Imperial College London between 2018 and 2021. We discuss how the course evolved from focusing solely on the linear MPC formulation to covering nonlinear MPC and some of its extensions. We also present a novel specification-based summative assessment framework, written in MATLAB, that was developed to assess the knowledge and understanding of the students in the course by tasking them with designing a controller for a real-world problem. The MATLAB assessment framework was designed to provide the students with the freedom to design and implement any MPC controller they wanted. The submitted controllers were then assessed against over 30 variations of the real-world problem to gauge student understanding of design robustness and the MPC topics from the course.
Nita L, Vila EMG, Zagorowska M, et al., 2022, Fast and accurate method for computing non-smooth solutions to constrained control problems, European Control Conference, Publisher: IEEE
Introducing flexibility in the time-discretisation mesh can improve convergence and computational time when solving differential equations numerically, particularly when the solutions are discontinuous, as commonly found in control problems with constraints. State-of-the-art methods use fixed mesh schemes, which cannot achieve superlinear convergence in the presence of non-smooth solutions. In this paper, we propose using a flexible mesh in an integrated residual method. The locations of the mesh nodes are introduced as decision variables, and constraints are added to set upper and lower bounds on the size of the mesh intervals. We compare our approach to a uniform fixed mesh on a real-world satellite reorientation example. This example demonstrates that the flexible mesh enables the solver to automatically locate the discontinuities in the solution, has superlinear convergence and faster solve times, while achieving the same accuracy as a fixed mesh.
O'Dwyer E, Kerrigan EC, Falugi P, et al., 2022, Data-driven predictive control with reduced computational effort and improved performance using segmented trajectories, Publisher: ArXiv
A class of data-driven control methods has recently emerged based on Willems'fundamental lemma. Such methods can ease the modelling burden in control designbut can be sensitive to disturbances acting on the system under control. Inthis paper, we extend these methods to incorporate segmented predictiontrajectories. The proposed segmentation enables longer prediction horizons tobe used in the presence of unmeasured disturbance. Furthermore, a computationtime reduction can be achieved through segmentation by exploiting the problemstructure, with computation time scaling linearly with increasing horizonlength. The performance characteristics are illustrated in a set-point trackingcase study in which the segmented formulation enables more consistentperformance over a wide range of prediction horizons. The computation time forthe segmented formulation is approximately half that of an unsegmentedformulation for a horizon of 100 samples. The method is then applied to abuilding energy management problem, using a detailed simulation environment, inwhich we seek to minimise the discomfort and energy of a 6-room apartment. Withthe segmented formulation, a 72% reduction in discomfort and 5% financial costreduction is achieved, compared to an unsegmented formulation using aone-day-ahead prediction horizon.
Biggs B, McInerney I, Kerrigan EC, et al., 2022, High-level synthesis using the Julia language, 2nd Workshop on Languages, Tools, and Techniques for Accelerator Design (LATTE’22)
The growing proliferation of FPGAs and High-level Synthesis (HLS) tools hasled to a large interest in designing hardware accelerators for complexoperations and algorithms. However, existing HLS toolflows typically require asignificant amount of user knowledge or training to be effective in bothindustrial and research applications. In this paper, we propose using the Julialanguage as the basis for an HLS tool. The Julia HLS tool aims to decrease thebarrier to entry for hardware acceleration by taking advantage of thereadability of the Julia language and by allowing the use of the existing largelibrary of standard mathematical functions written in Julia. We present aprototype Julia HLS tool, written in Julia, that transforms Julia code to VHDL.We highlight how features of Julia and its compiler simplified the creation ofthis tool, and we discuss potential directions for future work.
McInerney I, Kerrigan E, Constantinides G, 2022, Horizon-independent preconditioner design for linear predictive control, IEEE Transactions on Automatic Control, ISSN: 0018-9286
First-order optimization solvers, such as the Fast Gradient Method, are increasingly being used to solve Model Predictive Control problems in resource-constrained environments. Unfortunately, the convergence rate of these solvers is significantly affected by the conditioning of the problem data, with ill-conditioned problems requiring a large number of iterations. To reduce the number of iterations required, we present a simple method for computing a horizon-independent preconditioning matrix for the Hessian of the condensed problem. The preconditioner is based on the block Toeplitz structure of the Hessian. Horizon-independence allows one to use only the predicted system and cost matrices to compute the preconditioner, instead of the full Hessian. The proposed preconditioner has equivalent performance to an optimal preconditioner in numerical examples, producing speedups between 2x and 9x for the Fast Gradient Method. Additionally, we derive horizon-independent spectral bounds for the Hessian in terms of the transfer function of the predicted system, and show how these can be used to compute a novel horizon-independent bound on the condition number for the preconditioned Hessian.
Nie Y, Kerrigan E, 2022, Solving dynamic optimization problems to a specified accuracy: an alternating approach using integrated residuals, IEEE Transactions on Automatic Control, ISSN: 0018-9286
We propose a novel direct transcription and solution method for solving nonlinear, continuous-time dynamic optimization problems. Instead of forcing the dynamic constraints to be satisfied only at a selected number of points as in direct collocation, the new approach alternates between minimizing and constraining the squared norm of the dynamic constraint residuals integrated along the whole solution trajectories. As a result, the method can 1) obtain solutions of higher accuracy for the same mesh compared to direct collocation methods, 2) enables a flexible trade-off between solution accuracy and optimality, 3) provides reliable solutions for challenging problems, including those with singular arcs and high-index differential algebraic equations.
Falugi P, O’Dwyer E, Zagorowska MA, et al., 2022, MPC and optimal design of residential buildings with seasonal storage: a case study, Active Building Energy Systems, Editors: Doyle, Publisher: Springer International Publishing, Pages: 129-160, ISBN: 9783030797416
Residential buildings account for about a quarter of the global energy use. As such, residential buildings can play a vital role in achieving net-zero carbon emissions through efficient use of energy and balance of intermittent renewable generation. This chapter presents a co-design framework for simultaneous optimisation of the design and operation of residential buildings using Model Predictive Control (MPC). The adopted optimality criterion maximises cost savings under time-varying electricity prices. By formulating the co-design problem using model predictive control, we then show a way to exploit the use of seasonal storage elements operating on a yearly timescale. A case study illustrates the potential of co-design in enhancing flexibility and self-sufficiency of a system operating on multiple timescales. In particular, numerical results from a low-fidelity model report approximately doubled bill savings and carbon emission reduction compared to the a priori sizing approach.
Faqir OJ, Kerrigan EC, Gunduz D, 2021, Accuracy-awareness: A pessimistic approach to optimal control of triggered mobile communication networks, 7th IFAC Conference on Nonlinear Model Predictive Control (NMPC), Publisher: ELSEVIER, Pages: 296-301, ISSN: 2405-8963
We use nonlinear model predictive control to procure a joint control of mobility and transmission to minimize total network communication energy use. The nonlinear optimization problem is solved numerically in a self-triggered framework, where the next control update time depends on the predicted state trajectory and the accuracy of the numerical solution. Solution accuracy must be accounted for in any circumstance where systems are run in open-loop for long stretches of time based on potentially inaccurate predictions. These triggering conditions allow us to place wireless nodes in low energy ‘idle’ states for extended periods, saving over 70% of energy compared to a periodic policy where nodes consistently use energy to receive control updates.
Falugi P, O'Dwyer E, Kerrigan EC, et al., 2021, Predictive control co-design for enhancing flexibility in residential housing with battery degradation, 7th IFAC Conference on Nonlinear Model Predictive Control, Publisher: Elsevier, Pages: 8-13, ISSN: 2405-8963
Buildings are responsible for about a quarter of global energy-related CO2 emissions. Consequently, the decarbonisation of the housing stock is essential in achieving net-zero carbon emissions. Global decarbonisation targets can be achieved through increased efficiency in using energy generated by intermittent resources. The paper presents a co-design framework for simultaneous optimal design and operation of residential buildings using Model Predictive Control (MPC). The framework is capable of explicitly taking into account operational constraints and pushing the system to its efficiency and performance limits in an integrated fashion. The optimality criterion minimises system cost considering time-varying electricity prices and battery degradation. A case study illustrates the potential of co-design in enhancing flexibility and self-sufficiency of a system operating under different conditions. Specifically, numerical results from a low-fidelity model show substantial carbon emission reduction and bill savings compared to an a-priori sizing approach.
McInerney I, Nita L, Nie Y, et al., 2021, Towards a framework for nonlinear predictive control using derivative-free optimization, 7th IFAC Conference on Nonlinear Model Predictive Control, Publisher: Elsevier, Pages: 284-289, ISSN: 2405-8963
The use of derivative-based solvers to compute solutions to optimal control problems with non-differentiable cost or dynamics often requires reformulations or relaxations that complicate the implementation or increase computational complexity. We present an initial framework for using the derivative-free Mesh Adaptive Direct Search (MADS) algorithm to solve Nonlinear Model Predictive Control problems with non-differentiable features without the need for reformulation. The MADS algorithm performs a structured search of the input space by simulating selected system trajectories and computing the subsequent cost value. We propose handling the path constraints and the Lagrange cost term by augmenting the system dynamics with additional states to compute the violation and cost value alongside the state trajectories, eliminating the need for reconstructing the state trajectories in a separate phase. We demonstrate the practicality of this framework by solving a robust rocket control problem, where the objective is to reach a target altitude as close as possible, given a system with uncertain parameters. This example uses a non-differentiable cost function and simulates two different system trajectories simultaneously, with each system having its own free final time.
O’Dwyer E, Atam E, Falugi P, et al., 2021, A modelling workflow for predictive control in residential buildings, Active Building Energy Systems, Editors: Doyle, Publisher: Springer International Publishing, Pages: 99-128, ISBN: 9783030797416
Despite a large body of research, the widespread application of Model Predictive Control (MPC) to residential buildings has yet to be realised. The modelling challenge is often cited as a significant obstacle. This chapter establishes a systematic workflow, from detailed simulation model development to control-oriented model generation to act as a guide for practitioners in the residential sector. The workflow begins with physics-based modelling methods for analysis and evaluation. Following this, model-based and data-driven techniques for developing low-complexity, control-oriented models are outlined. Through sections detailing these different stages, a case study is constructed, concluding with a final section in which MPC strategies based on the proposed methods are evaluated, with a price-aware formulation producing a reduction in operational space-heating cost of 11%. The combination of simulation model development, control design and analysis in a single workflow can encourage a more rapid uptake of MPC in the sector.
Rodriguez Bernuz JM, McInerney I, Junyent Ferre A, et al., 2021, Design of a linear time-varying Model Predictive Control energy regulator for grid-tied VSCs, IEEE Transactions on Energy Conversion, Vol: 36, Pages: 1425-1434, ISSN: 0885-8969
This paper presents an energy regulator based on a Model Predictive Control (MPC) algorithm for a Voltage Source Converter (VSC). The MPC is formulated to optimise the converter performance according to the weights defined in an objective function that trades off additional features, such as current harmonic distortion, reactive power tracking and DC bus voltage oscillation. Differently from most approaches found in the research literature, the MPC proposed here considers the coupling dynamics between the AC and DC sides of the VSC. This study is focused on the example case of a single-phase VSC, which presents a nonlinear relationship between its AC and DC sides and a sustained double-line frequency power disturbance in its DC bus. To reduce the burden of the MPC, the controller is formulated to benefit from the slow energy dynamics of the system. Thus, the cascaded structure typically used in the control of VSCs is kept and the MPC is set as an energy regulator at a reduced sampling frequency while the current control relies on a fast inner controller. The computational burden of the algorithm is further reduced by using a linear time-varying approximation. The controller is presented in detail and experimental validation showing the performance of the algorithm is provided.
Atam E, Abdelmaguid TF, Keskin ME, et al., 2021, A hybrid green energy-based framework with a multi-objective optimization approach for optimal frost prevention in horticulture, Publisher: arXiv
In this paper, first we propose a novel hybrid renewable energy-basedsolution for frost prevention in horticulture applications involving activeheaters. Then, we develop a multi-objective robust optimization-basedformulation to optimize the distribution of a given number of active heaters ina given large-scale orchard. The objectives are to optimally heat the orchardby the proposed frost prevention system and to minimize the total length of theenergy distribution pipe network (which is directly related to the installationcost and the cost of energy losses during energy transfer). Next, the resultingoptimization problem is approximated using a discretization scheme. A casestudy is provided to give an idea of the potential savings using the proposedoptimization method compared to the result from a heuristic-based design, whichshowed a 24.13% reduction in the total pipe length and a 54.29% increase infrost prevention.
Faqir O, Kerrigan E, 2021, Mesh refinement for event-triggered nonlinear model predictive control, 21st IFAC World Congress, Publisher: IFAC Secretariat, Pages: 6516-6521, ISSN: 2405-8963
We consider the effect of using approximate system predictions in event-triggeredcontrol schemes. Such approximations often result from numerical transcription methods forsolving continuous-time optimal control problems. Mesh refinement schemes guarantee upperbounds on the error in the differential equations used to model system dynamics. In particular,we show that with the accuracy guarantees of a mesh refinement scheme, then event-triggeringschemes based on bounding the difference between predicted and measured state can be usedwith a guaranteed strictly positive inter-update time. We determine a lower bound for this timeand show that additional knowledge of the employed transcription method and evaluation ofthe approximation errors may be used to obtain better online estimates of inter-update times.This is the first work to consider using the solution accuracy of an optimal control problem asa metric for triggering new control updates.
Neuenhofen MP, Kerrigan E, 2021, A direct method for solving integral penalty transcriptions of optimal control problems, IEEE Conference on Decision and Control, Publisher: IEEE, Pages: 4822-4827
We present a numerical method for the minimization of objectives that are augmented with large quadratic penalties of overdetermined inconsistent equality constraints. Such objectives arise from quadratic integral penalty methods for the direct transcription of equality constrained optimal control problems. The Augmented Lagrangian Method (ALM) has a number of advantages over the Quadratic Penalty Method (QPM) for solving this class of problems. However, if the equality constraints of the discretization are inconsistent, then ALM might not converge to a point that minimizes the unconstrained bias of the objective and penalty term. Therefore, in this paper we explore a modification of ALM that fits our purpose. Numerical experiments demonstrate that the modified ALM can minimize certain quadratic penalty-augmented functions faster than QPM, whereas the unmodified ALM converges to a minimizer of a significantly different problem.
Kerrigan E, Nie Y, Faqir O, et al., 2021, Direct transcription for dynamic optimization: a tutorial with a case study on dual-patient ventilation during the COVID-19 pandemic, 59th IEEE Conference on Decision and Control 2020, Publisher: IEEE, Pages: 2597-2614
A variety of optimal control, estimation, system identification and design problems can be formulated as functional optimization problems with differential equality and inequality constraints. Since these problems are infinite-dimensional and often do not have a known analytical solution, one has to resort to numerical methods to compute an approximate solution. This paper uses a unifying notation to outline some of the techniques used in the transcription step of simultaneous direct methods (which discretize-then-optimize) for solving continuous-time dynamic optimization problems. We focus on collocation, integrated residual and Runge-Kutta schemes. These transcription methods are then applied to a simulation case study to answer a question that arose during the COVID-19 pandemic, namely: If there are not enough ventilators, is it possible to ventilate more than one patient on a single ventilator? The results suggest that it is possible, in principle, to estimate individual patient parameters sufficiently accurately, using a relatively small number of flow rate measurements, without needing to disconnect a patient from the system or needing more than one flow rate sensor. We also show that it is possible to ensure that two different patients can indeed receive their desired tidal volume, by modifying the resistance experienced by the air flow to each patient and controlling the ventilator pressure.
Neuenhofen MP, Kerrigan E, 2021, An integral penalty-barrier direct transcription method for optimal control, 59th IEEE Conference on Decision and Control 2020, Publisher: IEEE, Pages: 456-463
Some direct transcription methods can fail to converge, e.g. when there are singular arcs. We recently introduced a convergent direct transcription method for optimal control problems, called the penalty-barrier finite element method (PBF). PBF converges under very weak assumptions on the problem instance. PBF avoids the ringing between collocation points, for example, by avoiding collocation entirely. Instead, equality path constraint residuals are forced to zero everywhere by an integral quadratic penalty term.We highlight conceptual differences between collocation- and penalty-type direct transcription methods. Theoretical convergence results for both types of methods are reviewed and compared. Formulas for implementing PBF are presented, with details on the formulation as a nonlinear program (NLP), sparsity and solution. Numerical experiments compare PBF against several collocation methods with regard to robustness, accuracy, sparsity and computational cost. We show that the computational cost, sparsity and construction of the NLP functions are roughly the same as for orthogonal collocation methods of the same degree and mesh. As an advantage, PBF converges in cases where collocation methods fail. PBF also allows one to trade off computational cost, optimality and violation of differential and other equality equations against each other.
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, ISSN: 2054-5703
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.
Nie Y, Kerrigan E, 2020, Efficient Implementation of Rate Constraints for Nonlinear Optimal Control, IEEE Transactions on Automatic Control, ISSN: 0018-9286
We propose a general approach to directly implement rate constraints on the discretization mesh for all collocation methods, for both state and input variables. Unlike conventional approaches that may lead to singular control arcs, the solution of this on-mesh implementation has better properties. Moreover, computational speedups of more than 30% can be achieved by exploiting the properties of the resulting linear constraint equations.
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.
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