Prediction-Based Control of Linear Systems by Compensating Input-Dependent Input Delay of Integral-Type

International audienceThis study addresses the problem of delay compensation via a predictor-based output feedback for a class of linear systems subject to input delay which itself depends on the input. The equation defining the delay is implicit and involves past values of the input through an integral relation, the kernel of which is a polynomial function of the input. This modeling represents systems where transport phenomena take place at the inlet of a system involving a nonlinearity, which frequently occurs in the processing industry. The conditions of asymptotic stabilization require the magnitude of the feedback gain to comply with the initial conditions. Arguments for the proof of this novel result include general Halanay inequalities for delay differential equations and take advantage of recent advances in backstepping techniques for uncertain or varying delay systems

Modelling crop hail damage footprints with single-polarization radar: the roles of spatial resolution, hail intensity, and cropland density

Hail represents a major threat to agriculture in Switzerland, and assessments of current and future hail risk are of paramount importance for decision-making in the insurance industry and the agricultural sector. However, relating observational information on hail with crop-specific damage is challenging. Here, we build and systematically assess an open-source model to predict hail damage footprints for field crops (wheat, maize, barley, rapeseed) and grapevine from the operational radar product Maximum Expected Severe Hail Size (MESHS) at different spatial resolutions. To this end, we combine the radar information with detailed geospatial information on agricultural land use and geo-referenced damage data from a crop insurer for 12 recent hail events in Switzerland. We find that for field crops model skill gradually increases when the spatial resolution is reduced from 1 km down to 8 km. For even lower resolutions, the skill is diminished again. In contrast, for grapevine, decreasing model resolution below 1 km tends to reduce skill, which is attributed to the different spatial distribution of field crops and grapevine in the landscape. It is shown that identifying a suitable MESHS thresholds to model damage footprints always involves trade-offs. For the lowest possible MESHS threshold (20 mm) the model predicts damage about twice as often as observed (high frequency bias and false alarm ratio), but it also has a high probability of detection (80 %). The frequency bias decreases for larger thresholds and reaches an optimal value close to 1 for MESHS thresholds of 30–40 mm. However, this comes at the cost of a substantially lower probability of detection (around 50 %), while overall model skill, as measured by the Heidke skill score (HSS), remains largely unchanged (0.41–0.44). We argue that, ultimately, the best threshold therefore depends on the relative costs of a false alarm versus a missed event. Finally, the frequency of false alarms is substantially reduced and skill is improved (HSS = 0.54) when only areas with high cropland density are considered. Results from this simple, open-source model show that modelling of hail damage footprints to crops from single-polarization radar in Switzerland is skilful and is best done at 8 km resolution for field crops and 1 km for grapevine.</p

Projected impact of heat on mortality and labour productivity under climate change in Switzerland

Extreme temperatures have reached unprecedented levels in many regions of the globe due to climate change, and a further increase is expected. Besides other consequences, high temperatures increase the mortality risk and severely affect the labour productivity of workers. We perform a high-resolution spatial analysis to assess the impacts of heat on mortality and labour productivity in Switzerland and project their development under different Representative Concentration Pathway (RCP) scenarios, considering that no socio-economic changes take place. The model is based on the risk framework of the Intergovernmental Panel on Climate Change (IPCC), which combines the three risk components: hazard, exposure, and vulnerability. We model the two impact categories in the same spatially explicit framework, and we integrate uncertainties into the analysis by a Monte Carlo simulation. We model first that about 658 deaths are associated with heat exposure currently each year in Switzerland. Second, the economic costs caused by losses in labour productivity amount to around CHF 665 million (approx. USD 700 million) per year. Should we remain on an RCP8.5 emissions pathway, these values may double (for mortality) or even triple (for labour productivity) by the end of the century. Under an RCP2.6 scenario impacts are expected to slightly increase and peak around mid-century, when climate is assumed to stop warming. Even though uncertainties in the model are large, the underlying trend in impacts is unequivocal. The results of the study are valuable information for political discussions and allow for a better understanding of the cost of inaction

Compressible primitive equation: formal derivation and stability of weak solutions

We present a formal derivation of a simplified version of Compressible Primitive Equations (CPEs) for atmosphere modeling. They are obtained from $3$-D compressible Navier-Stokes equations with an \emph{anisotropic viscous stress tensor} where viscosity depends on the density. We then study the stability of the weak solutions of this model by using an intermediate model, called model problem, which is more simple and practical, to achieve the main result

Stability with respect to domain of the low Mach number limit of compressible viscous fluids

We study the asymptotic limit of solutions to the barotropic Navier-Stokes system, when the Mach number is proportional to a small parameter \ep \to 0 and the fluid is confined to an exterior spatial domain \Omega_\ep that may vary with \ep. As $\epsilon \rightarrow 0$, it is shown that the fluid density becomes constant while the velocity converges to a solenoidal vector field satisfying the incompressible Navier-Stokes equations on a limit domain. The velocities approach the limit strongly (a.a.) on any compact set, uniformly with respect to a certain class of domains. The proof is based on spectral analysis of the associated wave propagator (Neumann Laplacian) governing the motion of acoustic waves.Comment: 32 page

Projections and uncertainties of winter windstorm damage in Europe in a changing climate

Winter windstorms are among the most significant natural hazards in Europe linked to fatalities and substantial damage. However, projections of windstorm impact in Europe under climate change are highly uncertain. This study combines climate projections from 30 general circulation models participating in Phase 6 of the Coupled Model Intercomparison Project (CMIP6) with the climate risk assessment model CLIMADA to obtain projections of windstorm-induced damage over Europe in a changing climate. We conduct an uncertainty–sensitivity analysis and find large uncertainties in the projected changes in the damage, with climate model uncertainty being the dominant factor of uncertainty in the projections. We investigate the spatial patterns of the climate change-induced modifications in windstorm damage and find an increase in the damage in northwestern and northern central Europe and a decrease over the rest of Europe, in agreement with an eastward extension of the North Atlantic storm track into Europe. We combine all 30 available climate models in an ensemble-of-opportunity approach and find evidence for an intensification of future climate windstorm damage, in which damage with return periods of 100 years under current climate conditions becomes damage with return periods of 28 years under future SSP585 climate scenarios. Our findings demonstrate the importance of climate model uncertainty for the CMIP6 projections of windstorms in Europe and emphasize the increasing need for risk mitigation due to extreme weather in the future.</p

Large-scale risk assessment on snow avalanche hazard in alpine regions

Snow avalanches are recurring natural hazards that affect the population and infrastructure in mountainous regions, such as in the recent avalanche winters of 2018 and 2019, when considerable damage was caused by avalanches throughout the Alps. Hazard decision makers need detailed information on the spatial distribution of avalanche hazards and risks to prioritize and apply appropriate adaptation strategies and mitigation measures and thus minimize impacts. Here, we present a novel risk assessment approach for assessing the spatial distribution of avalanche risk by combining large-scale hazard mapping with a state-of-the-art risk assessment tool, where risk is understood as the product of hazard, exposure and vulnerability. Hazard disposition is modeled using the large-scale hazard indication mapping method RAMMS::LSHIM (Rapid Mass Movement Simulation::Large-Scale Hazard Indication Mapping), and risks are assessed using the probabilistic Python-based risk assessment platform CLIMADA, developed at ETH Zürich. Avalanche hazard mapping for scenarios with a 30-, 100- and 300-year return period is based on a high-resolution terrain model, 3 d snow depth increase, automatically determined potential release areas and protection forest data. Avalanche hazard for 40 000 individual snow avalanches is expressed as avalanche intensity, measured as pressure. Exposure is represented by a detailed building layer indicating the spatial distribution of monetary assets. The vulnerability of buildings is defined by damage functions based on the software EconoMe, which is in operational use in Switzerland. The outputs of the hazard, exposure and vulnerability analyses are combined to quantify the risk in spatially explicit risk maps. The risk considers the probability and intensity of snow avalanche occurrence, as well as the concentration of vulnerable, exposed buildings. Uncertainty and sensitivity analyses were performed to capture inherent variability in the input parameters. This new risk assessment approach allows us to quantify avalanche risk over large areas and results in maps displaying the spatial distribution of risk at specific locations. Large-scale risk maps can assist decision makers in identifying areas where avalanche hazard mitigation and/or adaption is needed.</p

Recent Advances Concerning Certain Class of Geophysical Flows

This paper is devoted to reviewing several recent developments concerning certain class of geophysical models, including the primitive equations (PEs) of atmospheric and oceanic dynamics and a tropical atmosphere model. The PEs for large-scale oceanic and atmospheric dynamics are derived from the Navier-Stokes equations coupled to the heat convection by adopting the Boussinesq and hydrostatic approximations, while the tropical atmosphere model considered here is a nonlinear interaction system between the barotropic mode and the first baroclinic mode of the tropical atmosphere with moisture. We are mainly concerned with the global well-posedness of strong solutions to these systems, with full or partial viscosity, as well as certain singular perturbation small parameter limits related to these systems, including the small aspect ratio limit from the Navier-Stokes equations to the PEs, and a small relaxation-parameter in the tropical atmosphere model. These limits provide a rigorous justification to the hydrostatic balance in the PEs, and to the relaxation limit of the tropical atmosphere model, respectively. Some conditional uniqueness of weak solutions, and the global well-posedness of weak solutions with certain class of discontinuous initial data, to the PEs are also presented.Comment: arXiv admin note: text overlap with arXiv:1507.0523

Singular Cucker-Smale Dynamics

The existing state of the art for singular models of flocking is overviewed, starting from microscopic model of Cucker and Smale with singular communication weight, through its mesoscopic mean-filed limit, up to the corresponding macroscopic regime. For the microscopic Cucker-Smale (CS) model, the collision-avoidance phenomenon is discussed, also in the presence of bonding forces and the decentralized control. For the kinetic mean-field model, the existence of global-in-time measure-valued solutions, with a special emphasis on a weak atomic uniqueness of solutions is sketched. Ultimately, for the macroscopic singular model, the summary of the existence results for the Euler-type alignment system is provided, including existence of strong solutions on one-dimensional torus, and the extension of this result to higher dimensions upon restriction on the smallness of initial data. Additionally, the pressureless Navier-Stokes-type system corresponding to particular choice of alignment kernel is presented, and compared - analytically and numerically - to the porous medium equation

A mathematical model for unsteady mixed flows in closed water pipes

We present the formal derivation of a new unidirectional model for unsteady mixed flows in non uniform closed water pipe. In the case of free surface incompressible flows, the \FS-model is formally obtained, using formal asymptotic analysis, which is an extension to more classical shallow water models. In the same way, when the pipe is full, we propose the \Pres-model, which describes the evolution of a compressible inviscid flow, close to gas dynamics equations in a nozzle. In order to cope the transition between a free surface state and a pressured (i.e. compressible) state, we propose a mixed model, the \PFS-model, taking into account changes of section and slope variation