A Parametric Non-Convex Decomposition Algorithm for Real-Time and Distributed NMPC

A novel decomposition scheme to solve parametric non-convex programs as they arise in Nonlinear Model Predictive Control (NMPC) is presented. It consists of a fixed number of alternating proximal gradient steps and a dual update per time step. Hence, the proposed approach is attractive in a real-time distributed context. Assuming that the Nonlinear Program (NLP) is semi-algebraic and that its critical points are strongly regular, contraction of the sequence of primal-dual iterates is proven, implying stability of the sub-optimality error, under some mild assumptions. Moreover, it is shown that the performance of the optimality-tracking scheme can be enhanced via a continuation technique. The efficacy of the proposed decomposition method is demonstrated by solving a centralised NMPC problem to control a DC motor and a distributed NMPC program for collaborative tracking of unicycles, both within a real-time framework. Furthermore, an analysis of the sub-optimality error as a function of the sampling period is proposed given a fixed computational power.Comment: 16 pages, 9 figure

A Parametric Multi-Convex Splitting Technique with Application to Real-Time NMPC

A novel splitting scheme to solve parametric multiconvex programs is presented. It consists of a fixed number of proximal alternating minimisations and a dual update per time step, which makes it attractive in a real-time Nonlinear Model Predictive Control (NMPC) framework and for distributed computing environments. Assuming that the parametric program is semi-algebraic and that its KKT points are strongly regular, a contraction estimate is derived and it is proven that the sub-optimality error remains stable if two key parameters are tuned properly. Efficacy of the method is demonstrated by solving a bilinear NMPC problem to control a DC motor.Comment: To appear in Proceedings of the 53rd IEEE Conference on Decision and Control 201

Soil hydraulic properties of a Nitisol in Kabete, Kenya

Water relations are among the most important physical phenomena that affect the use of soils for agricultural, ecological, environmental, and engineering purposes. To formulate soil-water relationships, soil hydraulic properties are required as essential inputs. The most important hydraulic properties are the soil-water retention curve and the hydraulic conductivity. The objective of this study was to determine the soil hydraulic properties of a Nitisol, at Kabete Campus Field Station. Use of an internal drainage procedure to characterize the hydraulic properties and soil and water retention curves allowed for the establishment of the moisture and matric potential at field capacity and permanent wilting point. The Bt2 (84 -115) and Bt3 (115 - 143 cm) had the highest clay contents of 619 compared to Ap, AB and Bt1 horizons. The PWP was attained at soil moisture contents of 0.223, 0.284, 0277, 0.307 and 0.314 m3m-3 in the Ap, AB, Bt1, Bt2, and Bt3 horizons, respectively. Horizontal saturated hydraulic conductivity (Ksat) was high at 6.0 cm hr-1 in Ap horizon and decreased to 0.4 cm hr-1 in the subsurface horizon (Bt3). Ksat in the vertical direction was higher than horizontal and ranged from 8.3 cm hr-1 in surface layer to 0.6 cm hr-1 in Bt3 horizon, with exception of Bt1 and Bt2 where horizontal Ksat was greater than vertical. The Ap horizon also had the highest crop extractable water. Though the AB and Bt1 had the same water content at low matric suction, the variation was very wide as the SWRC approached saturation point. Bt1 and Bt2 also had similar water contents at suction range of – 7kPa after which Bt1, tended towards Bt3. Bt3 had the narrowest range of crop extractable water and thus was attributed to texture. The Bt3 retained the most amount of water at 0.314 m3m-3concluding that θPWP increased with depth. The total available water capacity between FC and PWP in the profile was 79.2 mm m-1. The study observed that the field capacity, crop available water contents and hydraulic conductivities were influenced positively by soil organic matter. The Van Genuchten parameters of air entry value (α) and pore size distribution (n) indicated that pore size distribution was not even in the AP and AB horizons. The field capacity was attained at higher matric potential at -5kPa for Bt1 while Bt2 and AP, AB, Bt2 and Bt3 was at -10kPa.The functional relationship, K(θ) = aθb that deals with water redistribution as a result of soil hydraulic properties and evaporative demand of the atmosphere was highly correlated to soil moisture content and texture with R2 values > 0.85

On the scaling behaviour of cross-tie domain wall structures in patterned NiFe elements

The cross-tie domain wall structure in micrometre and sub-micrometre wide patterned elements of NiFe, and a thickness range of 30 to 70nm, has been studied by Lorentz microscopy. Whilst the basic geometry of the cross-tie repeat units remains unchanged, their density increases when the cross-tie length is constrained to be smaller than the value associated with a continuous film. This occurs when element widths are sufficiently narrow or when the wall is forced to move close to an edge under the action of an applied field. To a very good approximation the cross-tie density scales with the inverse of the distance between the main wall and the element edge. The experiments show that in confined structures, the wall constantly modifies its form and that the need to generate, and subsequently annihilate, extra vortex/anti-vortex pairs constitutes an additional source of hysteresis.Comment: 4 pages, 5 figures, accepted for publication in Europhysics Letters (EPL

X-ray photoelectron emission microscopy in combination with x-ray magnetic circular dichroism investigation of size effects on field-induced N\'eel-cap reversal

X-ray photoelectron emission microscopy in combination with x-ray magnetic circular dichroism is used to investigate the influence of an applied magnetic field on N\'eel caps (i.e., surface terminations of asymmetric Bloch walls). Self-assembled micron-sized Fe(110) dots displaying a moderate distribution of size and aspect ratios serve as model objects. Investigations of remanent states after application of an applied field along the direction of N\'eel-cap magnetization give clear evidence for the magnetization reversal of the N\'eel caps around 120 mT, with a $\pm$20 mT dispersion. No clear correlation could be found between the value of the reversal field and geometrical features of the dots