Electron beam stabilization in a synchrotron is a disturbance rejection problem, with hundreds of inputs and outputs, that is sampled at frequencies higher than 10 kHz. In this feasibility study, we focus on the practical issues of an efficient implementation of model predictive control (MPC) for the heavily ill-conditioned plant of the electron beam stabilization problem. To obtain a tractable control problem that can be solved using only a few iterations of the fast gradient method, we investigate different methods for preconditioning the resulting optimization problem and relate our findings to standard regularization techniques from crossdirectional control. We summarize the single-and multi-core implementations of our control algorithm on a digital signal processor (DSP), and show that MPC can be executed at the rate required for synchrotron control. MPC overcomes various problems of standard electron beam stabilization techniques, and the successful implementation can increase the stability of photon beams in synchrotron light sources.

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The higher-order generalized singular value decomposition (HO-GSVD) is a matrix factorization technique that extends the GSVD to N ≥ 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 ∈ R m i ×n as A i = U i Σ i V 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.

A method to bound the maximum energy perturbation for which regional stability of transitional fluid flow models can be guaranteed is introduced. The proposed method exploits the fact that the fluid model's nonlinearities are both lossless and locally bounded and uses the axes lengths of the ellipsoids for the trajectory set containment as variables in the stability conditions. Compared to existing approaches, the proposed method leads to an average increase in the maximum allowable energy perturbation of ≈ 29% for the Waleffe-Kim-Hamilton (WKH) shear flow model and of ≈ 38% for the 9-state reduced model of Couette flow.

There is a growing debate on whether the future of feedback control systems will be dominated by data-driven or model-driven approaches. Each of these two approaches has their own complimentary set of advantages and disadvantages, however, only limited attempts have, so far, been developed to bridge the gap between them. To address this issue, this paper introduces a method to bound the worst-case error between feedback control policies based upon model predictive control (MPC) and neural networks (NNs). This result is leveraged into an approach to automatically synthesize MPC policies minimising the worst-case error with respect to a NN. Numerical examples highlight the application of the bounds, with the goal of the paper being to encourage a more quantitative understanding of the relationship between data-driven and model-driven control.