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Raphael Keusch


Last Name

Keusch

First Name

Raphael

ORCID

0000-0001-5790-6709

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2021 - 20244
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Publications 1 - 4 of 4
  • Long-Horizon Direct Model Predictive Control for Power Converters With State Constraints
    Item type: Journal Article
    Keusch, Raphael; Loeliger, Hans-Andrea; Geyer, Tobias (2024)
    IEEE Transactions on Control Systems Technology
    The article explores a new approach to model predictive control (MPC) where both discrete-level input con-straints and state constraints are expressed in terms of Gaussian variables with unknown variances. The computations boil down to repeating Kalman-type recursions, with linear complexity in the prediction horizon. In consequence, the proposed approach can handle long prediction horizons with both discrete-level input constraints and state constraints, which has been a largely unresolved problem. The article demonstrates and evaluates the application of this approach by applying it to the control problem of a three-level power converter with an LC filter. In this application, long horizons are mandatory to obtain low harmonic current distortions, and certain state constraints must be imposed to prevent damage to the converter. The proposed controller can easily handle 100 or more time steps and is shown to perform remarkably well, not only in the steady state, but also in transients and in the case of a phase-to-ground fault.
  • Binary Control and Digital-to-Analog Conversion Using Composite NUV Priors and Iterative Gaussian Message Passing
    Item type: Conference Paper
    Keusch, Raphael; Malmberg, Hampus; Loeliger, Hans-Andrea (2021)
    ICASSP 2021 - 2021 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)
    The paper proposes a new method to determine a binary control signal for an analog linear system such that the state, or some output, of the system follows a given target trajectory. The method can also be used for digital-to-analog conversion.The heart of the proposed method is a new binary-enforcing NUV prior (normal with unknown variance). The resulting computations, for each planning period, amount to iterating forward-backward Gaussian message passing recursions (similar to Kalman smoothing), with a complexity (per iteration) that is linear in the planning horizon. In consequence, the proposed method is not limited to a short planning horizon.
  • Multiuser MIMO detection with composite NUV priors
    Item type: Conference Paper
    Marti, Gian; Keusch, Raphael; Loeliger, Hans-Andrea (2021)
    2021 11th International Symposium on Topics in Coding (ISTC)
    Normals with unknown variances (NUV) representations encompass variational representations of sparsifying norms and priors for sparse Bayesian learning. Recently, a binarizing NUV prior has been proposed and shown to work very well on certain approximation problems. We elaborate on this new prior and begin to explore its use for recovery problems. Concretely, we apply the method to the multiuser multiple-input multiple-output (MIMO) detection problem. Empirically, the method outperforms existing approaches based on convex relaxations and is more robust than a method based on approximate message-passing.
  • Composite NUV Priors and Applications
    Item type: Doctoral Thesis
    Keusch, Raphael (2022)
    Normal with unknown variance (NUV) priors are a central idea of sparse Bayesian learning and allow variational representations of non-Gaussian priors. More specifically, such variational representations can be seen as parameterized Gaussians, wherein the parameters are generally unknown. The advantage is apparent: for fixed parameters, NUV priors are Gaussian, and hence computationally compatible with Gaussian models. Moreover, working with (linear-)Gaussian models is particularly attractive since the Gaussian distribution is closed under affine transformations, marginalization, and conditioning. Interestingly, the variational representation proves to be rather universal than restrictive: many common sparsity-promoting priors (among them, in particular, the Laplace prior) can be represented in this manner. In estimation problems, parameters or variables of the underlying model are often subject to constraints (e.g., discrete-level constraints). Such constraints cannot adequately be represented by linear-Gaussian models and generally require special treatment. To handle such constraints within a linear-Gaussian setting, we extend the idea of NUV priors beyond its original use for sparsity. In particular, we study compositions of existing NUV priors, referred to as composite NUV priors, and show that many commonly used model constraints can be represented in this way. In Part I, we derive composite NUV representations of discretizing constraints, which enforce a model variable to take on values in a finite set (e.g., binary: {0,1}, or M-ary: {0,1,...,M−1}). Furthermore, we derive composite NUV representations of linear inequality constraints, which enforce a model variable to be lower-bounded, upper-bounded, or both. In addition, we derive a composite NUV representation of an exclusion constraint, which enforces a model variable to stay outside of an exclusion region. In Part II, we review the standard linear state space representation to model physical systems. Linear state space models (LSSMs) are defined only by a few parameters, bring flexible modeling capabilities, and pave the way for efficient algorithms thanks to their linearity and recursive structure. Kalman-type algorithms are commonly used to perform inference in Gaussian LSSMs. We will use a Gaussian message passing scheme based on factor graphs which offers several improvements and can be seen as a generalization of the standard Kalman filter/smoother. In particular, we will apply the modified Bryson-Frazier (MBF) smoother (augmented with input estimation), which is numerically stable and avoids matrix inversions. The expressive power of composite NUV priors and their computational compatibility with Gaussian models allow us to reformulate a variety of (constrained) optimization problems as statistical estimation problems in a linear-Gaussian model with unknown parameters. We propose an efficient iterative algorithm based on Gaussian message passing with closed-form update rules for the unknown parameters. An asset of the algorithm is the linear computational complexity in time (per iteration). Consequently, the method is able to efficiently handle long time horizons, which is generally the bottleneck of other algorithms. Finally, in Part III and IV, we demonstrate the applicability of the proposed method using pertinent problems from signal processing and constrained control. We consider problems ranging from digital-to-analog conversion, discrete-phase beamforming, trajectory planning, to obstacle avoidance, power converter control, and more. The results are promising and suggest that the proposed method is a versatile toolbox to handle various challenging practical applications.
Publications 1 - 4 of 4