Fast Gradient Method for Model Predictive Control with Input Rate and Amplitude Constraints

This paper is concerned with the computing efficiency of model predictive control (MPC) problems for dynamical systems with both rate and amplitude constraints on the inputs. Instead of augmenting the decision variables of the underlying finite-horizon optimal control problem to accommodate the input rate constraints, we propose to solve this problem using the fast gradient method (FGM), where the projection step is solved using Dykstra's algorithm. We show that, relative to the Alternating Direction of Method Multipliers (ADMM), this approach greatly reduces the computation time while halving the memory usage. Our algorithm is implemented in C and its performance demonstrated using several examples.Comment: Initial IFAC 2020 conference submissio

Control of Cross-Directional Systems using the Generalised Singular Value Decomposition

Diamond Light Source produces synchrotron radiation by accelerating electrons to relativistic speeds. In order to maximise the intensity of the radiation, vibrations of the electron beam are attenuated by a multi-input multi-output (MIMO) control system actuating hundreds of magnets at kilohertz rates. For future accelerator configurations, in which two separate arrays of magnets with different bandwidths are used in combination, standard accelerator control design methods based on the singular value decomposition (SVD) of the system gain matrix are not suitable. We therefore propose to use the generalised singular value decomposition (GSVD) to decouple a two-array cross-directional (CD) system into sets of two-input single-output (TISO) and single-input single-output (SISO) systems. We demonstrate that the two-array decomposition is linked to a single-array system, which is used to accommodate ill-conditioned systems and compensate for the non-orthogonality of the GSVD. The GSVD-based design is implemented and validated through real-world experiments at Diamond. Our approach provides a natural extension of single-array methods and has potential application in other CD systems, including paper making, steel rolling or battery manufacturing processes

A Higher-Order Generalized Singular Value Decomposition for Rank Deficient Matrices

The higher-order generalized singular value decomposition (HO-GSVD) is a matrix factorization technique that extends the GSVD to $N \ge 2$ data matrices, and can be used to identify shared subspaces in multiple large-scale datasets with different row dimensions. The standard HO-GSVD factors $N$ matrices $A_i\in\mathbb{R}^{m_i\times n}$ as $A_i=U_i\Sigma_i V^\text{T}$, but requires that each of the matrices $A_i$ has full column rank. We propose a reformulation of the HO-GSVD that extends its applicability to rank-deficient data matrices $A_i$. If the matrix of stacked $A_i$ has full rank, we show that the properties of the original HO-GSVD extend to our reformulation. The HO-GSVD captures shared right singular vectors of the matrices $A_i$, and we show that our method also identifies directions that are unique to the image of a single matrix. We also extend our results to the higher-order cosine-sine decomposition (HO-CSD), which is closely related to the HO-GSVD. Our extension of the standard HO-GSVD allows its application to datasets with $m_i < n$, such as are encountered in bioinformatics, neuroscience, control theory or classification problems.Comment: 13 pages, 2 figure

Multi-Array Electron Beam Stabilization using Block-Circulant Transformation and Generalized Singular Value Decomposition

We introduce a novel structured controller design for the electron beam stabilization problem of the UK's national synchrotron light source. Because changes to the synchrotron will not allow the application of existing control approaches, we develop a novel method to diagonalize the multi-input multi-output (MIMO) system. A generalized singular value decomposition (GSVD) is used to simultaneously diagonalize the actuator response matrices, which is applicable to an arbitrary number of actuator dynamics in a cross-directional setting. The resulting decoupled systems are regulated using mid-ranged control and the controller gains derived as a function of the generalized singular values. In addition, we exploit the inherent block-circulant symmetry of the system. The performance of our controller is demonstrated using simulations that involve machine data

Evaluation of prognostic risk models for postoperative pulmonary complications in adult patients undergoing major abdominal surgery: a systematic review and international external validation cohort study

Background Stratifying risk of postoperative pulmonary complications after major abdominal surgery allows clinicians to modify risk through targeted interventions and enhanced monitoring. In this study, we aimed to identify and validate prognostic models against a new consensus definition of postoperative pulmonary complications. Methods We did a systematic review and international external validation cohort study. The systematic review was done in accordance with the Preferred Reporting Items for Systematic Reviews and Meta-Analyses guidelines. We searched MEDLINE and Embase on March 1, 2020, for articles published in English that reported on risk prediction models for postoperative pulmonary complications following abdominal surgery. External validation of existing models was done within a prospective international cohort study of adult patients (≥18 years) undergoing major abdominal surgery. Data were collected between Jan 1, 2019, and April 30, 2019, in the UK, Ireland, and Australia. Discriminative ability and prognostic accuracy summary statistics were compared between models for the 30-day postoperative pulmonary complication rate as defined by the Standardised Endpoints in Perioperative Medicine Core Outcome Measures in Perioperative and Anaesthetic Care (StEP-COMPAC). Model performance was compared using the area under the receiver operating characteristic curve (AUROCC). Findings In total, we identified 2903 records from our literature search; of which, 2514 (86·6%) unique records were screened, 121 (4·8%) of 2514 full texts were assessed for eligibility, and 29 unique prognostic models were identified. Nine (31·0%) of 29 models had score development reported only, 19 (65·5%) had undergone internal validation, and only four (13·8%) had been externally validated. Data to validate six eligible models were collected in the international external validation cohort study. Data from 11 591 patients were available, with an overall postoperative pulmonary complication rate of 7·8% (n=903). None of the six models showed good discrimination (defined as AUROCC ≥0·70) for identifying postoperative pulmonary complications, with the Assess Respiratory Risk in Surgical Patients in Catalonia score showing the best discrimination (AUROCC 0·700 [95% CI 0·683–0·717]). Interpretation In the pre-COVID-19 pandemic data, variability in the risk of pulmonary complications (StEP-COMPAC definition) following major abdominal surgery was poorly described by existing prognostication tools. To improve surgical safety during the COVID-19 pandemic recovery and beyond, novel risk stratification tools are required. Funding British Journal of Surgery Society