A Parallel Decomposition Scheme for Solving Long-Horizon Optimal Control Problems

We present a temporal decomposition scheme for solving long-horizon optimal control problems. In the proposed scheme, the time domain is decomposed into a set of subdomains with partially overlapping regions. Subproblems associated with the subdomains are solved in parallel to obtain local primal-dual trajectories that are assembled to obtain the global trajectories. We provide a sufficient condition that guarantees convergence of the proposed scheme. This condition states that the effect of perturbations on the boundary conditions (i.e., initial state and terminal dual/adjoint variable) should decay asymptotically as one moves away from the boundaries. This condition also reveals that the scheme converges if the size of the overlap is sufficiently large and that the convergence rate improves with the size of the overlap. We prove that linear quadratic problems satisfy the asymptotic decay condition, and we discuss numerical strategies to determine if the condition holds in more general cases. We draw upon a non-convex optimal control problem to illustrate the performance of the proposed scheme

Spatial Gradients of Intensity and Persistence of Soil Water Repellency Under Different Forest Types in Central Mexico

Organic residues release hydrophobic compounds to the soil that may induce soil water repellency (WR), which may inhibit infiltration andincrease runoff and soil loss rates. Although there are many studies on soil WR through the world, very few investigations have been con-ducted in Mexican areas. This paper studies the natural background of soil WR in soils from central Mexico under representative forest types,analyzing the spatial distribution of soil WR in relation with tree canopy, vegetation cover and main soil chemical (pH, CaCO3, organic Ccontent and exchangeable cations) and physical properties (texture). The water drop penetration time and the ethanol tests were used to assesspersistence and intensity of soil WR, respectively. Although soil WR was not related with soil properties, it decreased strongly from soil be-low the canopy of conifers to soil below oaks. When different types of vegetation cover were considered, the proportion of water-repellentsoil increased following the sequence: bare soil < shrubs and herbaceous plants < shrubs < trees from fir, fir-pine-oak and pine-oak forest.We found an inverse relation with distance to the tree trunks, contributing to create a patchy pattern of soil WR, with soils under the canopyof conifers showing the most severe WR levels. The spatial distribution of soil WR is also conditioned by microclimatic gradients, as per-sistence and intensity of soil WR were usually lower in shaded areas (upslope transects from the tree trunks), where soil moisture contentis expected to be higher on average through the year. Copyright © 2016 John Wiley & Sons, LtdMinisterio de Economía y Competitividad CGL2013-47862-C2-1-RMinisterio de Economía y Competitividad CGL 2012-38655-C04-0