Learning-based Moving Horizon Estimation through Differentiable Convex Optimization Layers

To control a dynamical system it is essential to obtain an accurate estimate of the current system state based on uncertain sensor measurements and existing system knowledge. An optimization-based moving horizon estimation (MHE) approach uses a dynamical model of the system, and further allows for integration of physical constraints on system states and uncertainties, to obtain a trajectory of state estimates. In this work, we address the problem of state estimation in the case of constrained linear systems with parametric uncertainty. The proposed approach makes use of differentiable convex optimization layers to formulate an MHE state estimator for systems with uncertain parameters. This formulation allows us to obtain the gradient of a squared and regularized output error, based on sensor measurements and state estimates, with respect to the current belief of the unknown system parameters. The parameters within the MHE problem can then be updated online using stochastic gradient descent (SGD) to improve the performance of the MHE. In a numerical example of estimating temperatures of a group of manufacturing machines, we show the performance of tuning the unknown system parameters and the benefits of integrating physical state constraints in the MHE formulation.Comment: This paper was accepted for presentation at the 4th Annual Conference on Learning for Dynamics and Control. The extended version here contains an additional appendix with more details on the numerical exampl

Rocking motion induced charging of C60 on h-BN/Ni(111)

One monolayer of C60 on one monolayer of hexagonal boron nitride on nickel is investigated by photoemission. Between 150 and 250 K the work function decreases and the binding energy of the highest occupied molecular orbital (HOMO) increases by approx. 100 meV. In parallel, the occupancy of the, in the cold state almost empty, lowest unoccupied molecular orbital (LUMO) changes by 0.4 electrons. This charge redistribution is triggered by onset of molecular rocking motion, i.e. by orientation dependent tunneling between the LUMO of C60 and the substrate. The magnitude of the charge transfer is large and cannot be explained within a single particle picture. It is proposed to involve electron-phonon coupling where C60- polaron formation leads to electron self-trapping.Comment: 15 pages, 4 figure

Fermi surfaces of single layer dielectrics on transition metals

Single sheets of hexagonal boron nitride on transition metals provide a model system for single layer dielectrics. The progress in the understanding of h-BN layers on transition metals of the last 10 years are shortly reviewed. Particular emphasis lies on the boron nitride nanomesh on Rh(111), which is a corrugated single sheet of h-BN, where the corrugation imposes strong lateral electric fields. Fermi surface maps of h-BN/Rh(111) and Rh(111) are compared. A h-BN layer on Rh(111) introduces no new bands at the Fermi energy, which is expected for an insulator. The lateral electric fields of h-BN nanomesh violate the conservation law for parallel momentum in photoemission and smear out the momentum distribution curves on the Fermi surface.Comment: 14 pages, 6 figures, 1 table, 1 equation, Accepted for publication in the Special Surface Science issue in honor of Gerhard Ertl's Nobel Priz

LQG for Constrained Linear Systems: Indirect Feedback Stochastic MPC with Kalman Filtering

We present an output feedback stochastic model predictive control (SMPC) approach for linear systems subject to Gaussian disturbances and measurement noise and probabilistic constraints on system states and inputs. The presented approach combines a linear Kalman filter for state estimation with an indirect feedback SMPC, which is initialized with a predicted nominal state, while feedback of the current state estimate enters through the objective of the SMPC problem. For this combination, we establish recursive feasibility of the SMPC problem due to the chosen initialization, and closed-loop chance constraint satisfaction thanks to an appropriate tightening of the constraints in the SMPC problem also considering the state estimation uncertainty. Additionally, we show that for specific design choices in the SMPC problem, the unconstrained linear-quadratic-Gaussian (LQG) solution is recovered if it is feasible for a given initial condition and the considered constraints. We demonstrate this fact for a numerical example, and show that the resulting output feedback controller can provide non-conservative constraint satisfaction.Comment: 7 pages, 1 figur

One-dimensional electronic structure of phosphorene chains

Phosphorene, a 2D allotrope of phosphorus, is technologically very appealing because of its semiconducting properties and narrow band gap. Further reduction of the phosphorene dimensionality may spawn exotic properties of its electronic structure, including lateral quantum confinement and topological edge states. Phosphorene atomic chains self-assembled on Ag(111) have recently been characterized structurally but were found by angle-resolved photoemission (ARPES) to be electronically 2D. We show that these chains, although aligned equiprobably to three directions of the Ag(111) surface, can be characterized by ARPES because the three rotational variants are separated in the angular domain. The dispersion of the phosphorus band measured along and perpendicular to the chains reveals pronounced electronic confinement resulting in a 1D band, flat and dispersionless perpendicular to the chain direction in momentum space. Our density functional theory calculations reproduce the 1D band for the experimentally determined structure of P/Ag(111). We predict a semiconductor-to-metal phase transition upon increasing the density of the chain array so that a 2D structure would be metallic