2023/03/28 by Raphael Keusch, Hans‐Andrea Loeliger, Keusch, Raphael +1
Biochemistry, Genetics and Molecular Biology · Engineering · #Advanced Control Systems Optimization #Control Systems and Identification #Eicosanoids and Hypertension Pharmacology #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Signal Processing (eess.SP) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.2303.15806
openalex publication_date 2023/03/28 · openalex created_date 2023/03/31 · openalex updated_date 2026/07/28
Normals with unknown variance (NUV) and, more generally, normals with unknown parameters (NUP) can represent many useful priors including Lp norms and other sparsifying priors, and they blend well with linear-Gaussian models and Gaussian message passing algorithms. In this paper, we elaborate on recently proposed NUP representations of half-space constraints, box constraints, and finite-level constraints. We then demonstrate the use of such NUP representations for exemplary applications in model predictive control with a variety of constraints on the input, the output, or the internal state of the controlled system. In such applications, the computations boil down to iterations of Kalman-type forward-backward recursions, with a complexity (per iteration) that is linear in the planning horizon. In consequence, this approach can handle long planning horizons, which distinguishes it from the prior art. For nonconvex constraints, this approach has no claim to optimality, but it is empirically very effective.