The Three-point Problem of The Median Line Turning Point: on the Solutions for the Sphere and Ellipsoid

The problem of determining turning points of median lines between states separated by sea is considered. The turning point is defined as the point with equidistance lines to two basepoints along the shoreline of one state and one basepoint in the adjacent state. For the sphere the equidistance lines are parts of great circles, and the problem is solved by closed formulas. For the ellipsoid the lines are defined along geodesics, and an iterative solution is presented

Convex modeling of energy buffers in power control applications

This paper describes modeling steps for presenting energy buffers as convex models in power control applications. Except obtaining the optimal control, the paper also shows how convex optimization can be used to simultaneously size the energy buffer while optimally controlling a trajectory following system. The energy buffers are capacitors and batteries with quadratic power losses, while the resulting convex problem is a semidefinite program. The convex modeling steps are described through a problem of optimal buffer sizing and control of a hybrid electric vehicle. The studied vehicle is a city bus driven along a perfectly known bus line. The paper also shows modeling steps for alternative convex models where power losses and power limits of the energy buffer are approximated. The approximated models show significant decrease in computation time without visible impact on the optimal result

Медико-социальная экспертиза

МЕДИКО-СОЦИАЛЬНАЯ ЭКСПЕРТИЗАОРГАНИЗАЦИЯ ЗДРАВООХРАНЕНИЯУЧЕБНО-МЕТОДИЧЕСКИЕ ПОСОБИЯСодержатся современные материалы по вопросам медико-социальной экспертизы. Предназначено для проведения лабораторных занятий

Engine on/off control for dimensioning hybrid electric powertrains via convex optimization

This paper presents a novel heuristic method for optimal control of mixed-integer problems that, for given feasible values of the integer variables, are convex in the rest of the variables. The method is based on Pontryagin's maximum principle and allows the problem to be solved using convex optimization techniques. The advantage of this approach is the short computation time for obtaining a solution near the global optimum, which may otherwise need very long computation time when solved by algorithms guaranteeing global optimum, such as dynamic programming (DP). In this paper, the method is applied to the problem of battery dimensioning and power split control of a plug-in hybrid electric vehicle (PHEV), where the only integer variable is the engine on/off control, but the method can be extended to problems with more integer variables. The studied vehicle is a city bus, which is driven along a perfectly known bus line with a fixed charging infrastructure. The bus can charge either at standstill or while driving along a tramline (slide in). The problem is approached in two different scenarios: First, only the optimal power split control is obtained for several fixed battery sizes; and second, both battery size and power split control are optimized simultaneously. Optimizations are performed over four different bus lines and two different battery types, giving solutions that are very close to the global optimum obtained by DP

Multi-Objective versus Single-Objective Models in Geodetic Network Optimization

Configuration of a network and observation weights plays an important role in designing and establishing a geodetic network. In this paper, we consider single- and multi-objective optimization models in some numerical investigation. The results illustrate that the reliability model yields the best results in view of internal and external reliability and achievable observation precision. This result we interpret as that the reliability criterion is more sensitive to the configuration of a network than any of the other criteria. We propose re-optimization of the network in the cases where very high (non-achievable) precision is required or when some conditions are not met in the optimization process

Dimensioning and Control of a Thermally Constrained Double Buffer Plug-in HEV Powertrain

This paper describes modeling steps to enable fast evaluation of performance and cost effectiveness of a plugin hybrid electric vehicle. The paper also shows how convex optimization can be used to dimension the vehicle powertrain while simultaneously controlling the energy buffer power. The method allows for optimal control of powertrain components that are subject to thermal constraints. The studied vehicle is a city bus driven along a perfectly known bus line. The bus is equipped with an engine-generator unit and an energy buffer consisting of an ultracapacitor and a battery. The engine generator unit and the energy buffer are modeled with quadratic power losses and are sized for two different charging scenarios. In the first scenario the bus can charge for a couple of seconds while standing still at bus stops, and in the second scenario the bus can charge for a couple of minutes before starting the route. In both scenarios, the ultracapacitor temperature is kept below a certain limit

Convex relaxations in the optimal control of electrified vehicles

When controlling the energy flow in electrified powertrains by means of convex optimization, the typically non-convex set of the original formulation needs to be relaxed to a convex super-set. In this paper we show that when using the backward simulation approach, where vehicle velocity is equal to the reference velocity, the global optimum of the original non-convex problem can be obtained by solving the relaxed convex problem. When vehicle velocity is kept as a state in the problem, in the so called forward simulation approach, we provide a condition for which, when satisfied, an agreement will be achieved between the solutions of the relaxed and the original problem

On Moho Determination by the Vening Meinesz-Moritz Technique

This chapter describes a theory and application of satellite gravity and altimetry data for determining Moho constituents (i.e. Moho depth and density contrast) with support from a seismic Moho model in a least-squares adjustment. It presents and applies the Vening Meinesz-Moritz gravimetric-isostatic model in recovering the global Moho features. Internal and external uncertainty estimates are also determined. Special emphasis is devoted to presenting methods for eliminating the so-called non-isostatic effects, i.e. the gravimetric signals from the Earth both below the crust and from partly unknown density variations in the crust and effects due to delayed Glacial Isostatic Adjustment as well as for capturing Moho features not related with isostatic balance. The global means of the computed Moho depths and density contrasts are 23.8±0.05 km and 340.5 ± 0.37 kg/m3, respectively. The two Moho features vary between 7.6 and 70.3 km as well as between 21.0 and 650.0 kg/m3. Validation checks were performed for our modeled crustal depths using a recently published seismic model, yielding an RMS difference of 4 km