A tree structure algorithm for optimal control problems with state constraints

We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function based on a novel formulation in the case of convex constraints. Then the Dynamic Programming approach is developed by a discretization in time leading to a tree structure in space derived by the controlled dynamics, taking into account the state constraints to cut several branches of the tree. Moreover, an additional pruning allows for the reduction of the tree complexity as for the case without state constraints. Since the method does not use an a priori space grid, no interpolation is needed for the reconstruction of the value function and the accuracy essentially relies on the time step h. These features permit a reduction in CPU time and in memory allocations. The synthesis of optimal feedback controls is based on the values on the tree and an interpolation on the values obtained on the tree will be necessary if a different discretization in the control space is adopted, e.g. to improve the accuracy of the method in the reconstruction of the optimal trajectories. Several examples show how this algorithm can be applied to problems in low dimension and compare it to a classical DP method on a grid

Estudio comparativo de la estructura de granizos

Se analiza la estructura cristalina de 57 granizos provenientes de tres tormentas severas ocurridas en la provincia de Mendoza durante el verano 1976-77. Se observan secciones delgadas de las piedras y se clasifica, en las diferentes tormentas, el tipo de embriones que iniciaron la formación del granizo. Se mide el tamaño y la orientación de los cristales en las distintas capas de varios granizos y se infiere la temperatura ambiente en la cual estos han crecido. Los resultados obtenidos, junto con los datos del radiosondeo y la información del radar, se utilizan para reconstruir posibles trayectorias de los granizos en la nube.The crystallographic structure of 57 hailstones from three severe storms, are analyzed. The hailstorms took place in Mendoza, during the summer 1976-77. Thin sections of the stones are studied and a classification of the hailstone embryo type are made. The size and orientation of the crystals in the hailstone layers indicate the ambient temperature on which the growth of the hailstones took place. The obtained results, together with radiosounding and radar data are used in order to get the hailstone trajectories in the clouds.Asociación Argentina de Geofísicos y Geodesta

Aptitud forrajera de líneas S2 originadas del híbrido Zea mays L. x Zea diploperennis I.

Nineteen Iines of forage com originated from the crossing among Zea mays x Zea diploperennis in the second year of self-fertilization were evaluated. The analyzed characteristics were: plant height, number of stems per plant ''. number of ears per plant', stem diameter and leaf I stem relationship. Rainfall and temperature conditions were optimum during the com cultivation cycle. It was found difference among Iines in all the evaluated characteristics. Lines 3 and 16 exceeded the average for all the forage attributes. Lines 5 and 15 w1thsimilar aptitud do not overcome leaf/stem relationship. The general combinity aptitude will be able to identify the lines with the upper value of digestible dry matter.Se analizaron 19 líneas de maíz forrajero originadas a partir del cruzamiento entre Zea mays L. x Zea diploperennis l. en su segundo año de autofecundación (S2). Las características analizadas fueron: altura de planta, número de tallos por planta, número de mazorcas por planta, diámetro del tallo y la relación hoja/tallo. Las condiciones de precipitaciones y temperaturas fueron óptimas durante el ciclo del cultivo de maíz. Se encontró diferencia entre las líneas en todas las características evaluadas. Las líneas 3 y 16 superaron el promedio en todos los atributos forrajeros. Por su parte, la 5 y 15 también lo hicieron, aunque no superaron el promedio en la relación hoja/tallo. La evaluación de la Aptitud Combinatoria General permitiré identificar las líneas que maximicen la producción de materia seca digestible

Rendimiento de una red de observación de precipitaciones originadas en tormentas severas

Se caracteriza la conducta precipitante de -dos tormentas severas en la zona norte de Mendoza, a través de la información meteorológica sinóptica, y del relevamiento de caída de precipitación sólida que efectúa el Seguro Agrícola de la provincia, a través de la estimación de daños. Se realiza el mismo trabajo con la información que proporciona la mesored instalada, analizando en detalle las cualidades de la precipitación según sea sólida o líquida. Se estudia en particular la información provista por los “medidores de impacto", de los que se describe un procedimiento de calibración. Se juzga el comportamiento de la red instalada con respecto a su capacidad para tipificar la conducta de la precipitación asociada a la tormenta severa, sobre un área dada, en condiciones naturales. Se anticipa esta capacidad para el caso presunto de las condiciones artificialmente modificadas.The precipitating behavior of two severe storms at north of Mendoza is studied. This ¡s obtained on the basis of synoptic meteorological Information and hailstone damage evaluation performed by the Agricultura Insurance Office of Mendoza. The same work is carried out on the basis of the information provided by the installed network, by analyzing the precipitations quality in detail, according to its solid or liquid nature. Information provided by "hailpads" is especially studied; a procedure for calibration of "hailpads" is depicted. The network capability to characterize the behavior of precipitation associated to a severe storm, over a given area in natural conditions, is evaluated. This capability for the hypothetical case of artificially modified conditions, is advanced.Asociación Argentina de Geofísicos y Geodesta

An open, multi-vendor, multi-field-strength brain MR dataset and analysis of publicly available skull stripping methods agreement

This paper presents an open, multi-vendor, multi-field strength magnetic resonance (MR) T1-weighted volumetric brain imaging dataset, named Calgary-Campinas-359 (CC-359). The dataset is composed of images of older healthy adults (29-80 years) acquired on scanners from three vendors (Siemens, Philips and General Electric) at both 1.5 T and 3 T. CC-359 is comprised of 359 datasets, approximately 60 subjects per vendor and magnetic field strength. The dataset is approximately age and gender balanced, subject to the constraints of the available images. It provides consensus brain extraction masks for all volumes generated using supervised classification. Manual segmentation results for twelve randomly selected subjects performed by an expert are also provided. The CC-359 dataset allows investigation of 1) the influences of both vendor and magnetic field strength on quantitative analysis of brain MR; 2) parameter optimization for automatic segmentation methods; and potentially 3) machine learning classifiers with big data, specifically those based on deep learning methods, as these approaches require a large amount of data. To illustrate the utility of this dataset, we compared to the results of a supervised classifier, the results of eight publicly available skull stripping methods and one publicly available consensus algorithm. A linear mixed effects model analysis indicated that vendor (p - value < 0.001) and magnetic field strength (p - value < 0.001) have statistically significant impacts on skull stripping results170482494CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQCOORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIOR - CAPESFUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULO - FAPESP311228/2014-3; 157534/2015-488881.062158/2014-012013/07559-3; 2013/23514-0; 2016/18332-

Estudio comparativo de la estructura de granizos

Se analiza la estructura cristalina de 57 granizos provenientes de tres tormentas severas ocurridas en la provincia de Mendoza durante el verano 1976-77. Se observan secciones delgadas de las piedras y se clasifica, en las diferentes tormentas, el tipo de embriones que iniciaron la formación del granizo. Se mide el tamaño y la orientación de los cristales en las distintas capas de varios granizos y se infiere la temperatura ambiente en la cual estos han crecido. Los resultados obtenidos, junto con los datos del radiosondeo y la información del radar, se utilizan para reconstruir posibles trayectorias de los granizos en la nube.The crystallographic structure of 57 hailstones from three severe storms, are analyzed. The hailstorms took place in Mendoza, during the summer 1976-77. Thin sections of the stones are studied and a classification of the hailstone embryo type are made. The size and orientation of the crystals in the hailstone layers indicate the ambient temperature on which the growth of the hailstones took place. The obtained results, together with radiosounding and radar data are used in order to get the hailstone trajectories in the clouds.Asociación Argentina de Geofísicos y Geodesta

An efficient DP algorithm on a tree-structure for finite horizon optimal control problems

The classical dynamic programming (DP) approach to optimal control problems is based on the characterization of the value function as the unique viscosity solution of a Hamilton-Jacobi-Bellman equation. The DP scheme for the numerical approximation of viscosity solutions of Bellman equations is typically based on a time discretization which is projected on a fixed state-space grid. The time discretization can be done by a one-step scheme for the dynamics and the projection on the grid typically uses a local interpolation. Clearly the use of a grid is a limitation with respect to possible applications in high-dimensional problems due to the curse of dimensionality. Here, we present a new approach for finite horizon optimal control problems where the value function is computed using a DP algorithm with a tree structure algorithm constructed by the time discrete dynamics. In this way there is no need to build a fixed space triangulation and to project on it. The tree will guarantee a perfect matching with the discrete dynamics and drop off the cost of the space interpolation allowing for the solution of very high-dimensional problems. Numerical tests will show the effectiveness of the proposed method

Error Estimates for a Tree Structure Algorithm Solving Finite Horizon Control Problems*

In the dynamic programming approach to optimal control problems a crucial role is played by the value function that is characterized as the unique viscosity solution of a Hamilton-Jacobi-Bellman (HJB) equation. It is well known that this approach suffers from the "curse of dimensionality" and this limitation has reduced its use in real world applications. Here, we analyze a dynamic programming algorithm based on a tree structure to mitigate the "curse of dimensionality". The tree is built by the discrete time dynamics avoiding the use of a fixed space grid which is the bottleneck for highdimensional problems, this also drops the projection on the grid in the approximation of the value function. In this work, we present first order error estimates for the the approximation of the value function based on the tree-structure algorithm. The estimate turns out to have the same order of convergence of the numerical method used for the approximation of the dynamics. Furthermore, we analyze a pruning technique for the tree to reduce the complexity and minimize the computational effort. Finally, we present some numerical tests to show the theoretical results

High-order approximation of the finite horizon control problem via a tree structure algorithm

Solving optimal control problems via Dynamic Programming is a difficult task that suffers for the”curse of dimensionality”. This limitation has reduced its practical impact in real world applications since the construction of numerical methods for nonlinear PDEs in very high dimension is practically unfeasible. Recently, we proposed a new numerical method to compute the value function avoiding the construction of a space grid and the need for interpolation techniques. The method is based on a tree structure that mimics the continuous dynamics and allows to solve optimal control problems in high-dimension. This property is particularly useful to attack control problems with PDE constraints. We present a new high-order approximation scheme based on the tree structure and show some numerical results

A tree structure algorithm for optimal control problems with state constraints

We present a tree structure algorithm for optimal control problems with state constraints. We prove a convergence result for a discrete time approximation of the value function based on a novel formulation in the case of convex constraints. Then the Dynamic Programming approach is developed by a discretization in time leading to a tree structure in space derived by the controlled dynamics, taking into account the state constraints to cut several branches of the tree. Moreover, an additional pruning allows for the reduction of the tree complexity as for the case without state constraints. Since the method does not use an a priori space grid, no interpolation is needed for the reconstruction of the value function and the accuracy essentially relies on the time step h. These features permit a reduction in CPU time and in memory allocations. The synthesis of optimal feedback controls is based on the values on the tree and an interpolation on the values obtained on the tree will be necessary if a different discretization in the control space is adopted, e.g. to improve the accuracy of the method in the reconstruction of the optimal trajectories. Several examples show how this algorithm can be applied to problems in low dimension and compare it to a classical DP method on a grid