Imperial College London


Faculty of EngineeringDepartment of Electrical and Electronic Engineering

Professor of Control and Optimization



+44 (0)20 7594 6343e.kerrigan Website




Mrs Raluca Reynolds +44 (0)20 7594 6281




1114Electrical EngineeringSouth Kensington Campus





Publication Type

197 results found

Xia C, Zhang J, Kerrigan E, Rigas Get al., 2024, Active flow control for bluff body drag reduction using reinforcement learning with partial measurements, Journal of Fluid Mechanics, Vol: 981, ISSN: 0022-1120

Active flow control for drag reduction with reinforcement learning (RL) is performed in the wake of a two-dimensional square bluff body at laminar regimes with vortex shedding. Controllers parametrised by neural networks are trained to drive two blowing and suction jets that manipulate the unsteady flow. The RL with full observability (sensors in the wake) discovers successfully a control policy that reduces the drag by suppressing the vortex shedding in the wake. However, a non-negligible performance degradation ( ∼ 50 % less drag reduction) is observed when the controller is trained with partial measurements (sensors on the body). To mitigate this effect, we propose an energy-efficient, dynamic, maximum entropy RL control scheme. First, an energy-efficiency-based reward function is proposed to optimise the energy consumption of the controller while maximising drag reduction. Second, the controller is trained with an augmented state consisting of both current and past measurements and actions, which can be formulated as a nonlinear autoregressive exogenous model, to alleviate the partial observability problem. Third, maximum entropy RL algorithms (soft actor critic and truncated quantile critics) that promote exploration and exploitation in a sample-efficient way are used, and discover near-optimal policies in the challenging case of partial measurements. Stabilisation of the vortex shedding is achieved in the near wake using only surface pressure measurements on the rear of the body, resulting in drag reduction similar to that in the case with wake sensors. The proposed approach opens new avenues for dynamic flow control using partial measurements for realistic configurations.

Journal article

Zagorowska M, Falugi P, O'Dwyer E, Kerrigan Eet al., 2024, Automatic scenario generation for efficient solution of robust optimal control problems, International Journal of Robust and Nonlinear Control, Vol: 34, Pages: 1370-1396, ISSN: 1049-8923

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as large nonlinear optimization problems. The optimization problems are challenging to solve due to their size, especially if the control problems include time-varying uncertainty. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric and time-varying uncertainty. By iteratively adding interim worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. We show that the local reduction method for optimal control problems consists of solving a series of simplified optimal control problems to find worst-case constraint violations. In particular, we present examples where local reduction methods find worst-case scenarios that are not on the boundary of the uncertainty set. We also provide bounds on the error if local solvers are used. The proposed approach is illustrated with two case studies with parametric and additive time-varying uncertainty. In the first case study, the number of scenarios obtained from local reduction is 101, smaller than in the case when all 2¹⁴+³ₓ¹⁹² extreme scenarios are considered. In the second case study, the number of scenarios obtained from the local reduction is two compared to 512 extreme scenarios. Our approach was able to satisfy the constraints both for parametric uncertainty and time-varying disturbances, whereas approaches from literature either violated the constraints or became computationally expensive.

Journal article

Neuenhofen M, Kerrigan E, Nie Y, 2024, Numerical comparison of collocation vs quadrature penalty methods, 62nd IEEE Conference on Decision and Control, Publisher: IEEE, ISSN: 2576-2370

Direct transcription with collocation-type methods (CTM) is a popular approach for solvingdynamic optimization problems. It is known that thesetypes of methods can fail to converge for problems thatfeature singular-arc solutions, high-index differential-algebraic equations and over-determined constraints.Recently, we proposed the use of quadrature penaltymethods (QPM) as an alternative numerical approachto collocation-type methods. In contrast to the conceptof collocation, which requires constraint-residuals toequal zero at individual points (e.g. at collocationpoints), the main idea of QPM is to simply oversamplethis number of points and use their respective quadrature weights in a quadratic penalty term, coiningthe name of quadrature penalty. In this paper, weprovide numerical case studies and a broad numericalcomparison on a wide range of problems, highlightingthe benefits of QPM over CTM not only in difficultproblems, but also in solving problems competitively toCTM. These results show that QPM can be consideredan attractive first go-to method when solving generaldynamic optimization problems.

Conference paper

Faulwasser T, Kerrigan E, Logist F, Lucia S, Mönningmann M, Parisio A, Schulze Darup Met al., 2023, Teaching model predictive control: what, when, where, why, who, and how?, IEEE Control Systems, ISSN: 1066-033X

Over the course of four decades, model predictive control (MPC) has become one of the great success stories in systems and control. It has grown from its native habitat (chemical process control) into all domains of control applications – power and energy systems, mechatronics and robotics, as well as aerospace and aeronautics. Hence, in a modern systems and control curriculum, MPC triggers not so much the question of if it should be taught. In fact, industrial demand for and continued research potential of MPC suggest that one should rather ask the Aristotelian 5W1H (What, When, Where, Why, Who, and How?) about teaching MPC. This article presents insights to the 5Ws distilled from the results of a survey on teaching MPC conducted in the systems and control community. Moreover, the how is approached through blueprint suggestions for curricula for an undergraduate discrete-time linear quadratic MPC course and for graduate courses covering the continuous-time nonlinear avenue and the learning-based route.

Journal article

Sritharan L, Nita L, Kerrigan E, 2023, An efficient method for maximal area coverage in the context of a hierarchical controller for multiple unmanned aerial vehicles, European Journal of Control, Vol: 74, Pages: 1-6, ISSN: 0947-3580

Computing the exact area of the union of an arbitrary number of circles is a challenging problem, since the union is generally non-convex and may be composed of multiple non-overlapping regions. In this paper, we propose tackling this problem by using graph-theoretical concepts and Green’s Theorem for exact area computation. Moreover, we show the implementation of this method for a rapid area coverage application with unmanned aerial vehicles (UAVs). Maximizing the area covered using multiple agents is difficult because fast solutions to large-scale optimization problems are sought. In our solution method, we present a hierarchical control framework. On the upper layer, a high-level controller performs centralised computation to determine the optimal UAV locations to maximize the area covered. On the bottom level, we adopt a decentralised approach by implementing multiple local controllers to tackle the trajectory planning and collision avoidance for each agent individually using Nonlinear Model Predictive Control (NMPC). Numerical experiments show that our method for computing the covered area can reduce the computational time required to solve the optimal positioning problem by more than two orders of magnitude when compared to a Monte-Carlo method. The trajectory planning problem was tested for up to 13 agents and the run-time was on the order of milliseconds, demonstrating the suitability for real-time implementation of the presented framework.

Journal article

Ravera A, Oliveri A, Lodi M, Bemporad A, Heemels WPMH, Kerrigan E, Storace Met al., 2023, Co-design of a controller and its digital implementation: the MOBY-DIC2 toolbox for embedded model predictive control, IEEE Transactions on Control Systems Technology, Vol: 31, Pages: 2871-2878, ISSN: 1063-6536

Several software tools are available in the literaturefor the design and embedded implementation of linear model predictive control (MPC), both in its implicit and explicit (either exact or approximate) forms. Most of them generate C code for easy implementation on a microcontroller, and the others can convert the C code into hardware description language code for implementation on a field programmable gate array (FPGA). However, a unified tool allowing one to generate efficient embedded MPC for an FPGA, starting from the definition of the plant and its constraints, was still missing. The MOBY-DIC2 toolbox described in this brief bridges this gap. To illustrate its functionalities, the tool is exploited to embed the controllerand observer for a real buck power converter in an FPGA. This implementation achieves a latency of about 30 µs with the implicit controller and 240 μs with the approximate explicit controller.

Journal article

Zagorowska M, Falugi P, O'Dwyer E, Kerrigan ECet al., 2023, Automatic Scenario Generation for Robust Optimal Control Problems, Pages: 1229-1234

Existing methods for nonlinear robust control often use scenario-based approaches to formulate the control problem as nonlinear optimization problems. Increasing the number of scenarios improves robustness, while increasing the size of the optimization problems. Mitigating the size of the problem by reducing the number of scenarios requires knowledge about how the uncertainty affects the system. This paper draws from local reduction methods used in semi-infinite optimization to solve robust optimal control problems with parametric uncertainty. We show that nonlinear robust optimal control problems are equivalent to semi-infinite optimization problems and can be solved by local reduction. By iteratively adding interim globally worst-case scenarios to the problem, methods based on local reduction provide a way to manage the total number of scenarios. In particular, we show that local reduction methods find worst case scenarios that are not on the boundary of the uncertainty set. The proposed approach is illustrated with a case study with both parametric and additive time-varying uncertainty. The number of scenarios obtained from local reduction is 101, smaller than in the case when all 214+3×192 boundary scenarios are considered. A validation with randomly drawn scenarios shows that our proposed approach reduces the number of scenarios and ensures robustness even if local solvers are used.

Conference paper

Faqir O, Kerrigan E, 2023, Inaccuracy matters: Accounting for solution accuracy in event-triggered nonlinear model predictive control, IEEE Transactions on Automatic Control, Vol: 68, Pages: 3316-3330, 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.

Journal article

O'Dwyer E, Kerrigan E, Falugi P, Zagorowska M, Shah Net al., 2023, Data-driven predictive control with improved performance using segmented trajectories, IEEE Transactions on Control Systems Technology, Vol: 31, Pages: 1355-1365, ISSN: 1063-6536

A class of data-driven control methods has recently emerged based on Willems' fundamental lemma. Such methods can ease the modelling burden in control design but can be sensitive to disturbances acting on the system under control. In this paper, we extend these methods to incorporate segmented prediction trajectories. The proposed segmentation enables longer prediction horizons to be used in the presence of unmeasured disturbance. Furthermore, a computation time reduction can be achieved through segmentation by exploiting the problem structure, with computation time scaling linearly with increasing horizon length. The performance characteristics are illustrated in a set-point tracking case study in which the segmented formulation enables more consistent performance over a wide range of prediction horizons. The computation time for the segmented formulation is approximately half that of an unsegmented formulation for a horizon of 100 samples. The method is then applied to a building energy management problem, using a detailed simulation environment, in which we seek to minimise the discomfort and energy of a 6-room apartment. With the segmented formulation, a 72% reduction in discomfort and 5% financial cost reduction is achieved, compared to an unsegmented formulation using a one-day-ahead prediction horizon.

Journal article

Neuenhofen M, Kerrigan E, 2023, Solving problems with inconsistent constraints with a modified augmented lagrangian method, IEEE Transactions on Automatic Control, Vol: 68, Pages: 2592-2598, 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.

Journal article

Nita L, Kerrigan EC, Vila EMG, Nie Yet al., 2023, Solving optimal control problems with non-smooth solutions using an integrated residual method and flexible mesh, IEEE 61st Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 1211-1216, ISSN: 0743-1546

Conference paper

Nie Y, Kerrigan E, 2023, Solving dynamic optimization problems to a specified accuracy: an alternating approach using integrated residuals, IEEE Transactions on Automatic Control, Vol: 68, Pages: 548-555, 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.

Journal article

McInerney I, Kerrigan E, Constantinides G, 2023, Horizon-independent preconditioner design for linear predictive control, IEEE Transactions on Automatic Control, Vol: 68, Pages: 580-587, 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.

Journal article

McInerney I, Kerrigan EC, 2022, Teaching predictive control using specification-based summative assessments, 13th Symposium on Advances in Control Education, Publisher: Elsevier, Pages: 236-241, 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.

Conference paper

Nita L, Vila EMG, Zagorowska M, Kerrigan E, Nie Y, McInerney I, Falugi Pet al., 2022, Fast and accurate method for computing non-smooth solutions to constrained control problems, 2022 European Control Conference (ECC), Publisher: IEEE, Pages: 1049-1054

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.

Conference paper

O'Dwyer E, Falugi P, Shah N, Kerrigan Eet 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

Conference paper

McInerney I, 2022, Numerical methods for model predictive control

There has been an increased interest in controlling complex systems using Model Predictive Control (MPC). However, the use of resource-constrained computing platforms in these systems has slowed the adoption of MPC. This thesis focuses on increasing the efficiency of numerical methods for MPC in terms of resource usage and solution time, while also simplifying the design process. We first show how block Toeplitz operators can be used to link the linear MPC matrices to the transfer function of the predicted system, resulting in horizon-independent bounds on the condition number of the condensed Hessian and the upper iteration bound for the Fast Gradient Method (FGM). We derive a horizon-independent preconditioner that produces up to a 9x speedup for the FGM while reducing the preconditioner computation time by up to 50,000x compared to an existing preconditioner. We propose a new method for computing the minimum number of fractional bits needed to ensure the FGM with fixed-point arithmetic is stable, with an example showing decreases of up to 77% in resource usage and 50% in the computational energy when using this method on a Field Programmable Gate Array. Finally, we present a framework using the derivative-free Mesh Adaptive Direct Search method to solve nonlinear MPC problems with non-differentiable features or quantized variables without the need for complex or costly reformulations. We augment the system dynamics with additional states to compute the Lagrange cost term and the violation of the path constraints along the state trajectory, and then perform a structured search of the input space using a single-shooting simulation of the system dynamics. We demonstrate this framework on a robust Goddard rocket problem with a non-differentiable cost and a quantized thrust input, where we achieve an altitude within 40m of the target, while other methods are unable to get closer than 180m.

Thesis dissertation

Biggs B, McInerney I, Kerrigan EC, Constantinides GAet 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.

Conference paper

Falugi P, O’Dwyer E, Zagorowska MA, Atam E, Kerrigan EC, Strbac G, Shah Net 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.

Book chapter

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.

Conference paper

Falugi P, O'Dwyer E, Kerrigan EC, Atam E, Zagorowska M, Strbac G, Shah Net 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.

Conference paper

McInerney I, Nita L, Nie Y, Oliveri A, Kerrigan ECet 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.

Conference paper

O’Dwyer E, Atam E, Falugi P, Kerrigan EC, Zagorowska MA, Shah Net 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.

Book chapter

Rodriguez Bernuz JM, McInerney I, Junyent Ferre A, Kerrigan Eet 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.

Journal article

Atam E, Abdelmaguid TF, Keskin ME, Kerrigan ECet 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.

Working paper

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.

Conference paper

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.

Conference paper

Kerrigan E, Nie Y, Faqir O, Kennedy CH, Niederer SA, Solis-Lemus JA, Vincent P, Williams SEet 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.

Conference paper

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.

Conference paper

Nie Y, Kerrigan E, 2021, Efficient Implementation of Rate Constraints for Nonlinear Optimal Control, IEEE Transactions on Automatic Control, Vol: 66, Pages: 329-334, 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.

Journal article

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