How scaling of the disturbance set affects robust positively invariant sets for linear systems

This paper presents new results on robust positively invariant (RPI) sets for linear discrete-time systems with additive disturbances. In particular, we study how RPI sets change with scaling of the disturbance set. More precisely, we show that many properties of RPI sets crucially depend on a unique scaling factor which determines the transition from nonempty to empty RPI sets. We characterize this critical scaling factor, present an efficient algorithm for its computation, and analyze it for a number of examples from the literature

Implicit predictors in regularized data-driven predictive control

We introduce the notion of implicit predictors, which characterize the input-(state)-output prediction behavior underlying a predictive control scheme, even if it is not explicitly enforced as an equality constraint (as in traditional model or subspace predictive control). To demonstrate this concept, we derive and analyze implicit predictors for some basic data-driven predictive control (DPC) schemes, which offers a new perspective on this popular approach that may form the basis for modified DPC schemes and further theoretical insights.Comment: This paper is a reprint of a contribution to the IEEE Control Systems Letters. 6 pages, 2 figure

Nonuniversal transition to condensate formation in two-dimensional turbulence

The occurrence of system-scale coherent structures, so-called condensates, is a well-known phenomenon in two-dimensional turbulence. Here, the transition to condensate formation is investigated as a function of the magnitude of the force and for different types of forcing. Random forces with constant mean energy input lead to a supercritical transition, while forcing through a small-scale linear instability results in a subcritical transition with bistability and hysteresis. That is, the transition to condensate formation in two-dimensional turbulence is nonuniversal. For the supercritical case we quantify the effect of large-scale friction on the value of the critical exponent and the location of the critical point

Exact Markov Chain-based Runtime Analysis of a Discrete Particle Swarm Optimization Algorithm on Sorting and OneMax

Meta-heuristics are powerful tools for solving optimization problems whose structural properties are unknown or cannot be exploited algorithmically. We propose such a meta-heuristic for a large class of optimization problems over discrete domains based on the particle swarm optimization (PSO) paradigm. We provide a comprehensive formal analysis of the performance of this algorithm on certain "easy" reference problems in a black-box setting, namely the sorting problem and the problem OneMAX. In our analysis we use a Markov-model of the proposed algorithm to obtain upper and lower bounds on its expected optimization time. Our bounds are essentially tight with respect to the Markov-model. We show that for a suitable choice of algorithm parameters the expected optimization time is comparable to that of known algorithms and, furthermore, for other parameter regimes, the algorithm behaves less greedy and more explorative, which can be desirable in practice in order to escape local optima. Our analysis provides a precise insight on the tradeoff between optimization time and exploration. To obtain our results we introduce the notion of indistinguishability of states of a Markov chain and provide bounds on the solution of a recurrence equation with non-constant coefficients by integration

A deterministic view on explicit data-driven (M)PC

We show that the explicit realization of data-driven predictive control (DPC) for linear deterministic systems is more tractable than previously thought. To this end, we compare the optimal control problems (OCP) corresponding to deterministic DPC and classical model predictive control (MPC), specify its close relation, and systematically eliminate ambiguity inherent in DPC. As a central result, we find that the explicit solutions to these types of DPC and MPC are of exactly the same complexity. We illustrate our results with two numerical examples highlighting features of our approach.Comment: 7 pages, 2 figure, submitted to 61st IEE Conference on Decision and Control 202

Detailed mapping of lava and ash deposits at Indonesian volcanoes by means of VHR PlanetScope change detection

Mapping of lava flows in unvegetated areas of active volcanoes using optical satellite data is challenging due to spectral similarities of volcanic deposits and the surrounding background. Using very high-resolution PlanetScope data, this study introduces a novel object-oriented classification approach for mapping lava flows in both vegetated and unvegetated areas during several eruptive phases of three Indonesian volcanoes (Karangetang 2018/2019, Agung 2017, Krakatau 2018/2019). For this, change detection analysis based on PlanetScope imagery for mapping loss of vegetation due to volcanic activity (e.g., lava flows) is combined with the analysis of changes in texture and brightness, with hydrological runoff modelling and with analysis of thermal anomalies derived from Sentinel-2 or Landsat-8. Qualitative comparison of the mapped lava flows showed good agreement with multispectral false color time series (Sentinel-2 and Landsat-8). Reports of the Global Volcanism Program support the findings, indicating the developed lava mapping approach produces valuable results for monitoring volcanic hazards. Despite the lack of bands in infrared wavelengths, PlanetScope proves beneficial for the assessment of risk and near-real-time monitoring of active volcanoes due to its high spatial (3 m) and temporal resolution (mapping of all subaerial volcanoes on a daily basis)

Ferroelectricity and Crystal Phases in Mixed‐Cation Lead Iodide Perovskite Solar Cells

After the discovery of ferroelectricity in archetypal methylammonium lead iodide (MAPbI$_3$), the discussion arose, if more advanced derivatives thereof are also ferroelectric and to what extent the polar domains mitigate detrimental charge carrier recombination in perovskite solar cells. Herein, the A-site cation methylammonium is gradually substituted with formamidinium and cesium. The domain contrast measured by piezoresponse force microscopy is correlated with the distortion of the crystal structure measured by X-ray diffraction. By Rietveld analysis, a detailed structural model together with texture information is determinded, which reveals an intriguing interplay between lead iodide and the perovskite phases. Finally, the bearing of ferroelectric domains in mixed-cation perovskites on the solar cell performance is discussed