This paper deals with model predictive control problems for large scale dynamical systems with cyclic symmetry. Based on the properties of block circulant matrices, we introduce a complex-valued coordinate transformation that block diagonalizes and truncates the original finite-horizon optimal control problem. Using this coordinate transformation, we develop a modified alternating direction method of multipliers (ADMM) algorithm for general constrained quadratic programs with block circulant blocks. We test our modified algorithm in two different simulated examples and show that our coordinate transformation significantly increases the computation speed.

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Background The manufacturing of any standard mechanical ventilator cannot rapidly be upscaled to several thousand units per week, largely due to supply chain limitations. The aim of this study was to design, verify and perform a pre-clinical evaluation of a mechanical ventilator based on components not required for standard ventilators, and that met the specifications provided by the Medicines and Healthcare Products Regulatory Agency (MHRA) for rapidly-manufactured ventilator systems (RMVS). Methods The design utilises closed-loop negative feedback control, with real-time monitoring and alarms. Using a standard test lung, we determined the difference between delivered and target tidal volume (VT) at respiratory rates between 20 and 29 breaths per minute, and the ventilator's ability to deliver consistent VT during continuous operation for >14 days (RMVS specification). Additionally, four anaesthetised domestic pigs (3 male-1 female) were studied before and after lung injury to provide evidence of the ventilator's functionality, and ability to support spontaneous breathing. Findings Continuous operation lasted 23 days, when the greatest difference between delivered and target VT was 10% at inspiratory flow rates > 825 mL/s. In the pre-clinical evaluation, the VT difference was -1 (-90 to 88) mL [mean (LoA)], and positive end-expiratory pressure (PEEP) difference was -2 (-8 to 4) cmH 2 O. VT delivery being triggered by pressures below PEEP demonstrated spontaneous ventilation support. Interpretation The mechanical ventilator presented meets the MHRA therapy standards for RMVS and, being based on largely available components, can be manufactured at scale. Funding Work supported by Wellcome/EPSRC Centre for Medical Engineering,King’s Together Fund and Oxford University.

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.