Publications
197 results found
Abraham E, Kerrigan EC, 2015, Lower-Order H∞ Filter Design for Bilinear Systems With Bounded Inputs, Signal Processing, IEEE Transactions on, Vol: 63, Pages: 895-906, ISSN: 1053-587X
Jones BL, Kerrigan EC, Morrison JF, 2015, A modeling and filtering framework for the semi-discretised Navier-Stokes equations, Pages: 1215-1220
© 2009 EUCA. Spatial discretisation of fluid mechanical systems typically leads to descriptor systems consisting of large numbers of differential algebraic equations (DAEs). In an effort to apply standard control theory to such systems, physical insight is often used to analytically reformulate the DAE as an ordinary differential equation (ODE). In general, this is a difficult process that typically requires expert insight into specific systems, and so in this work we consider a more flexible numerical method that is straightforward to implement on any regular DAE. The numerical procedure is outlined and a new method for computing one of the steps is presented.With respect to Kalman filtering of descriptor systems, it is known in general that 'process noise' can sometimes not be added to all states owing to a violation of causality. In this paper we present a new method for computing the subspace of causal disturbances, suitable for large DAEs. Finally, the techniques developed in this paper are applied to the specific case of plane Poiseuille flow and it is shown how a standard state-space system is easily obtained that possesses a similar spectrum and pseudospectrum to the Orr-Somerfeld-Squire system.
Jerez JL, Goulart PJ, Richter S, et al., 2014, Embedded Online Optimization for Model Predictive Control at Megahertz Rates, IEEE Transactions on Automatic Control, Vol: 59, Pages: 3238-3251, ISSN: 0018-9286
Faster, cheaper, and more power efficient optimization solvers than those currently possible using general-purpose techniques are required for extending the use of model predictive control (MPC) to resource-constrained embedded platforms. We propose several custom computational architectures for different first-order optimization methods that can handle linear-quadratic MPC problems with input, input-rate, and soft state constraints. We provide analysis ensuring the reliable operation of the resulting controller under reduced precision fixed-point arithmetic. Implementation of the proposed architectures in FPGAs shows that satisfactory control performance at a sample rate beyond 1 MHz is achievable even on low-end devices, opening up new possibilities for the application of MPC on embedded systems.
Jerez JL, Goulart PJ, Richter S, et al., 2014, Embedded Online Optimization for Model Predictive Control at Megahertz Rates, IEEE TRANSACTIONS ON AUTOMATIC CONTROL, Vol: 59, Pages: 3238-3251, ISSN: 0018-9286
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- Citations: 158
Kerrigan EC, 2014, Co-design of Hardware and Algorithms for Real-time Optimization, 2014 European Control Conference (ECC), Publisher: IEEE, Pages: 2484-2489
It is difficult or impossible to separate the performance of an optimization solver from the architecture of the computing system on which the algorithm is implemented. This is particularly true if measurements from a physical system are used to update and solve a sequence of mathematical optimization problems in real-time, such as in control, automation, signal processing and machine learning. In these real-time optimization applications the designer has to trade off computing time, space and energy against each other, while satisfying constraints on the performance and robustness of the resulting cyber-physical system. This paper is an informal introduction to the issues involved when designing the computing hardware and a real-time optimization algorithm at the same time, which can result in systems with efficiencies and performances that are unachievable when designing the sub-systems independently. The co-design process can, in principle, be formulated as a sequence of uncertain and non-smooth optimization problems. In other words, optimizers might be used to design optimizers. Before this can become a reality, new systems theory and numerical methods will have to be developed to solve these co-design problems effectively and reliably.
Ge M, Kerrigan E, 2014, Noise Covariance Estimation for Time-varying and Nonlinear Systems, The 19th World Congress of the International Federation of Automatic Control
Hartley EN, Jerez JL, Suardi A, et al., 2014, Predictive control using an FPGA with application to aircraft control, IEEE Transactions on Control Systems Technology, Vol: 22, Pages: 1006-1017, ISSN: 1558-0865
Alternative and more efficient computational methodscan extend the applicability of MPC to systems with tightreal-time requirements. This paper presents a “system-on-a-chip”MPC system, implemented on a field programmable gate array(FPGA), consisting of a sparse structure-exploiting primal dualinterior point (PDIP) QP solver for MPC reference tracking anda fast gradient QP solver for steady-state target calculation. Aparallel reduced precision iterative solver is used to accelerate thesolution of the set of linear equations forming the computationalbottleneck of the PDIP algorithm. A numerical study of the effectof reducing the number of iterations highlights the effectivenessof the approach. The system is demonstrated with an FPGA-inthe-looptestbench controlling a nonlinear simulation of a largeairliner. This study considers many more manipulated inputsthan any previous FPGA-based MPC implementation to date,yet the implementation comfortably fits into a mid-range FPGA,and the controller compares well in terms of solution quality andlatency to state-of-the-art QP solvers running on a standard PC.
Ng BF, Hesse H, Palacios R, et al., 2014, Aeroservoelastic state-space vortex lattice modeling and load alleviation of wind turbine blades, Wind Energy, Vol: 18, Pages: 1317-1331, ISSN: 1095-4244
An aeroservoelastic model, capturing the structural response and the unsteady aerodynamics of turbine rotors, will be used to demonstrate the potential of active load alleviation using aerodynamic control surfaces. The structural model is a geometrically non-linear composite beam, which is linearized around equilibrium rotating conditions and coupled with time-domain aerodynamics given by a linearized 3D unsteady vortex lattice method. With much of the existing work relying on blade element momentum theory with various corrections, the use of the unsteady vortex lattice method in this paper seeks to complement and provide a direct higher fidelity solution for the unsteady rotor dynamics in attached flow conditions. The resulting aeroelastic model is in a state-space formulation suitable for control synthesis. Flaps are modeled directly in the vortex lattice description and using a reduced-order model of the coupled aeroelastic formulation, a linear-quadratic-Gaussian controller is synthesized and shown to reduce root mean square values of the root-bending moment and tip deflection in the presence of continuous turbulence. Similar trend is obtained when the controller is applied to the original non-linear model of the turbine. Trade-offs between reducing root-bending moment and suppressing the negative impacts on torsion due to flap deployment will also be investigated.
Jones BL, Kerrigan EC, Morrison JF, 2014, A modeling and filtering framework for the semi-discretised Navier-Stokes equations, Pages: 1215-1220
Spatial discretisation of fluid mechanical systems typically leads to descriptor systems consisting of large numbers of differential algebraic equations (DAEs). In an effort to apply standard control theory to such systems, physical insight is often used to analytically reformulate the DAE as an ordinary differential equation (ODE). In general, this is a difficult process that typically requires expert insight into specific systems, and so in this work we consider a more flexible numerical method that is straightforward to implement on any regular DAE. The numerical procedure is outlined and a new method for computing one of the steps is presented.With respect to Kalman filtering of descriptor systems, it is known in general that 'process noise' can sometimes not be added to all states owing to a violation of causality. In this paper we present a new method for computing the subspace of causal disturbances, suitable for large DAEs. Finally, the techniques developed in this paper are applied to the specific case of plane Poiseuille flow and it is shown how a standard state-space system is easily obtained that possesses a similar spectrum and pseudospectrum to the Orr-Somerfeld-Squire system.
Ahmed S, Kerrigan EC, 2014, Suboptimal predictive control for satellite detumbling, Journal of Guidance Control and Dynamics, Vol: 37, Pages: 850-859, ISSN: 1533-3884
Rate damping in the initial acquisition phase of a magnetically controlled small satellite is a big challenge for the control system. In this phase, the main difficulties are dynamic nonlinearities due to high body rates, time-varying control due to the change in Earth’s magnetic field, inherent underactuation, and constraints on available power. The control system is required to minimize the detumbling time with minimal use of onboard resources. In comparison to the existing control techniques used in the initial acquisition phase, predictive control can be considered a suitable choice for handling such conflicting objectives in the presence of constraints. In this work, performance of two existing nonlinear model predictive control schemes that guarantee closed-loop stability are analyzed. Nonlinear model predictive control gives improved performance by reducing the detumbling time compared to classical control techniques based on the rate of change of Earth’s magnetic field; however, the computational requirements are high. Furthermore, it is demonstrated that, when the body rates increase, the computational burden of nonlinear model predictive control to reach an optimal point becomes prohibitively large. For these situations, an algorithm is presented that allows early termination of the optimizer by imposing an additional constraint on the cost reduction. The early termination criteria of the optimizer can be chosen based on the available computational resources. The imposed cost reduction constraint also helps in further reducing the detumbling time. Extensive numerical simulations show that the presented algorithm works well in practice for a good range of initial body rates.
Feng Z, Kerrigan EC, 2014, Declutching control of wave energy converters using derivative-free optimization, Pages: 7647-7652, ISSN: 1474-6670
We propose a novel formulation for declutching control of wave energy converters with the power takeoff time as the only decision variable. The optimal control problem is modeled as a single-variable optimization problem, thereby making real-time implementation a possibility. We present a derivate-free optimization algorithm that exploits the quantization of the decision variable in order to reduce the number of function evaluations needed to compute a solution. We propose two receding horizon closed-loop strategies: the first one uses past wave information and can increase the energy generation by 42% compared to the uncontrolled case, while the second formulation uses predictions of future waves and results in a further 40% increase in energy generation. For irregular waves with peak periods longer than 6 s, one can generate at least four times more energy when co-designing the physical system and controller, compared to a controlled system that was optimized without a controller in the feedback loop.
Suardi A, Longo S, Kerrigan EC, et al., 2014, Robust explicit MPC design under finite precision arithmetic, 19th World Congress of the International-Federation-of-Automatic-Control (IFAC), Publisher: ELSEVIER SCIENCE BV, Pages: 2939-2944, ISSN: 2405-8963
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- Citations: 1
Longo S, Kerrigan EC, Constantinides GA, 2014, Constrained LQR for low-precision data representation, AUTOMATICA, Vol: 50, Pages: 162-168, ISSN: 0005-1098
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- Citations: 9
Ng BF, Hesse H, Palacios R, et al., 2014, Efficient Aeroservoelastic Modeling and Control using Trailing-Edge Flaps of Wind Turbines, United-Kingdom-Automatic-Control-Council (UKACC) 10th International Conference on Control (CONTROL), Publisher: IEEE, Pages: 1-6
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- Citations: 8
Drummond R, Jerez JL, Kerrigan EC, 2014, Gradient Filter Methods for Predictive Control with Simple Constraints, United-Kingdom-Automatic-Control-Council (UKACC) 10th International Conference on Control (CONTROL), Publisher: IEEE, Pages: 679-684
Jones C, Kerrigan E, 2013, Call for Papers: '<i>Predictive control for embedded systems</i>', OPTIMAL CONTROL APPLICATIONS & METHODS, Vol: 34, Pages: 504-504, ISSN: 0143-2087
Abraham E, Kerrigan EC, 2013, Optimal Active Control and Optimization of a Wave Energy Converter, IEEE Transactions on Sustainable Energy, Vol: 4, Pages: 324-332, ISSN: 1949-3029
Jerez JL, Goulart PJ, Richter S, et al., 2013, Embedded Predictive Control on an FPGA using the Fast Gradient Method, European Control Conference (ECC), Publisher: IEEE, Pages: 3614-3620
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- Citations: 27
Suardi A, Longo S, Kerrigan EC, et al., 2013, Energy-aware MPC co-design for DC-DC converters, European Control Conference (ECC), Publisher: IEEE, Pages: 3608-3613
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- Citations: 6
Hasan A, Kerrigan EC, Constantinides GA, 2012, Control-theoretic forward error analysis of iterative numericalalgorithms, IEEE Transactions on Automatic Control, Vol: 58, Pages: 1524-1529, ISSN: 0018-9286
It has been known for at least five decades that control theorycan be used to study iterative algorithms. However, little work can be foundin the control systems literature on numerical algorithms, especially on thestudy of finite precision effects. In this technical note, we consider numericaliterative algorithms in finite precision as dynamical systems and studythe effects of finite precision using control theory. By using the control toolsof input-to-state stability and results from the study of quantization in controlsystems, we present new systematic ways to find bounds on the forwarderror for iterative algorithms. The advantages of the proposed schemes areshown by applying them to find bounds for the classical iterative methodsfor solving a system of linear equations.
Shahzad A, Kerrigan EC, Constantinides GA, 2012, A Stable and Efficient Method for Solving a Convex Quadratic Program with Application to Optimal Control, SIAM Journal on Optimization, Vol: 22, Pages: 1369-1393, ISSN: 1052-6234
Jerez JL, Ling KV, Constantinides GA, et al., 2012, Model predictive control for deeply pipelined field-programmable gate array implementation: algorithms and circuitry, IET Control Theory and Applications, Vol: 6, Pages: 1029-1041, ISSN: 1751-8652
Model predictive control (MPC) is an optimisation-based scheme that imposes a real-time constraint on computingthe solution of a quadratic programming (QP) problem. The implementation of MPC in fast embedded systems presents newtechnological challenges. In this paper we present a parameterised field-programmable gate array implementation of acustomised QP solver for optimal control of linear processes with constraints, which can achieve substantial acceleration overa general purpose microprocessor, especially as the size of the optimisation problem grows. The focus is on exploiting thestructure and accelerating the computational bottleneck in a primal-dual interior-point method. We then introduce a new MPCformulation that can take advantage of the novel computational opportunities, in the form of parallel computational channels,offered by the proposed pipelined architecture to improve performance even further. This highlights the importance of theinteraction between the control theory and digital system design communities for the success of MPC in fast embedded systems.
Buchstaller D, Kerrigan EC, Constantinides GA, 2012, Sampling and controlling faster than the computational delay, IET Control Theory and Applications, Vol: 6, Pages: 1071-1079
Ahmed S, Kerrigan EC, Jaimoukha IJ, 2012, A Semidefinite Relaxation-Based Algorithm for Robust Attitude Estimation, IEEE Transactions on Signal Processing, Vol: 60, Pages: 3942-3952, ISSN: 1053-587X
This paper presents a tractable method for solving a robust attitude estimation problem, based on a weighted least squares approach with nonlinear constraints. Attitude estimation requires information of a few vector quantities, each obtained from both a sensor and a mathematical model. By considering the modeling errors, measurementnoise, sensor biases and offsets as infinity-norm bounded uncertainties, we formulate a robust optimization problem, which is non-convex with nonlinear cost and constraints. The robust min-max problem is approximated with a non-convex minimization problem using an upper bound. A new regularization scheme is also proposed to improve the robust performance. We then use semidefinite relaxation to convert the suboptimal problem with quadratic cost and constraints into a tractable semidefinite program with a linear objective function and linear matrix inequality constraints. We also show how to extract the solution of the suboptimal robust estimation problem from the solution of the semidefinite relaxation. Further, a mathematical proof supported by numerical results is presented stating the gap between the suboptimal problem and its relaxation is zero under a given condition, which is mostly true in real life scenarios. The usefulness of the proposed algorithm in the presence of uncertainties is evaluated with the helpof examples.
Ng BF, Palacios R, Graham JMR, et al., 2012, Robust control synthesis for gust load alleviation from large aeroelastic models with relaxation of spatial discretisation, European Wind Energy Association Annual Event, Copenhagen, Denmark
Jerez JL, Kerrigan EC, Constantinides GA, 2012, A sparse and condensed QP formulation for predictive control of LTI systems, Automatica, Vol: 48, Pages: 999-1002, ISSN: 1873-2836
The computational burden that model predictive control (MPC) imposes depends to a large extent on the way the optimal control problem is formulated as an optimization problem. We present a formulation where the input is expressed as an affine function of the state such that the closed-loop dynamics matrix becomes nilpotent. Using this approach and removing the equality constraints leads to a compact and sparse optimization problem to be solved at each sampling instant. The problem can be solved with a cost per interior-point iteration that is linear with respect to the horizon length, when this is bigger than the controllability index of the plant. The computational complexity of existing condensed approaches grow cubically with the horizon length, whereas existing non-condensed and sparse approaches also grow linearly, but with a greater proportionality constant than with the method presented here.
Kerrigan EC, Jerez JL, Longo S, et al., 2012, Number Representation in Predictive Control, IFAC Conference on Nonlinear Model Predictive Control 2012 (NMPC'12), Publisher: IFAC
We will present some of the lessons that we have learnt at Imperial College London while implementing predictive controllers on embedded systems. In particular, we will discusssome of the advantages and issues that arise when one does not use IEEE double-precisionoating-point to solve the resulting optimization problems, as well as some initial suggestions on how to overcome certain problems.
Jerez JL, Constantinides GA, Kerrigan EC, 2012, Fixed Point Lanczos: Sustaining TFLOP-equivalent Performance in FPGAs for Scientific Computing, 20th IEEE International Symposium on Field-Programmable Custom Computing Machines (FCCM), Publisher: IEEE, Pages: 53-60
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- Citations: 6
Jerez JL, Constantinides GA, Kerrigan EC, 2012, Towards a Fixed Point QP Solver for Predictive Control, 51st IEEE Annual Conference on Decision and Control (CDC), Publisher: IEEE, Pages: 675-680, ISSN: 0743-1546
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- Citations: 8
Hasan A, Kerrigan EC, Constantindes GA, 2011, Solving a positive definite system of linearequations via the matrix exponential, IEEE Control and Decision Conference
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