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

An Alternating Trust Region Algorithm for Distributed Linearly Constrained Nonlinear Programs, Application to the AC Optimal Power Flow

A novel trust region method for solving linearly constrained nonlinear programs is presented. The proposed technique is amenable to a distributed implementation, as its salient ingredient is an alternating projected gradient sweep in place of the Cauchy point computation. It is proven that the algorithm yields a sequence that globally converges to a critical point. As a result of some changes to the standard trust region method, namely a proximal regularisation of the trust region subproblem, it is shown that the local convergence rate is linear with an arbitrarily small ratio. Thus, convergence is locally almost superlinear, under standard regularity assumptions. The proposed method is successfully applied to compute local solutions to alternating current optimal power flow problems in transmission and distribution networks. Moreover, the new mechanism for computing a Cauchy point compares favourably against the standard projected search as for its activity detection properties

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

Strings of droplets propelled by coherent waves

Bouncing walking droplets possess fascinating properties due to their peculiar wave/particule interaction. In order to study such walkers in a 1d system, we considered the case of one or more droplets in an annular cavity. We show that, in this geometry, walking droplets form a string of synchronized bouncing droplets that share a common coherent wave propelling the group at a speed faster than single walkers. The formation of this coherent wave and the collective behavior of droplets is captured by a model.Comment: 5 Pages, 5 Figures, 2 supplementary movies (identical), supplementary .pdf fil

Effect of different cover crop residue management practices on soil moisture content under a tomato crop (Lycopersicon esculentum)

Water relations are among the most important physical phenomena that affect the use of soils for agricultural, ecological, environmental, and engineering purposes. In sub-Saharan African, water is most critical in limiting crop production and yields especially in the Arid and Sub-arid regions. The soil water storage, available water content and soil water balance under various cover crop residue management practices in a Nitisol were evaluated in a field experiment at the Kabete Field Station, University of Nairobi. The effects of surface mulching, above and below ground biomass and roots only incorporated of velvet bean (Mucuna pruriens), Tanzanian sunhemp (Crotalaria ochroleuca) and purple vetch (Vicia benghalensis) cover crops, fertilizer and non fertilized plots on soil water balance were studied. The experimental design was a split plot and tomato (Lycopersicon esculentum) was the test crop. Since water content was close to field capacity, the drainage component at 100 cm soil depth was negligible and evapotranspiration was therefore derived from the change in soil moisture storage and precipitation. Residue management showed that above and below ground biomass incorporated optimized the partitioning of the water balance components, increasing moisture storage, leading to increased tomato yields and water use efficiency (WUE). Furthermore, vetch above and below ground biomass incorporated significantly improved the quantity and frequency of deep percolation. Soil fertilization (F) and non fertilization (NF) caused the most unfavourable partitioning of water balance, leading to the lowest yield and WUE. Tomato yields ranged from 4.1 in NF to 7.4 Mg ha-1 in vetch treated plots. Vetch above and belowground biomass incorporated had significant (p ≤ 0.1) yields of 11.4 Mg ha-1 compared to all other residue management systems. Vetch residue treatment had the highest WUE (22.7 kg mm-1 ha-1) followed by mucuna treated plots (20.7 kg mm-1 ha-1) and both were significantly different (p ≤ 0.05) compared to the others irrespective of residue management practices

Resonant and antiresonant bouncing droplets

When placed onto a vibrating liquid bath, a droplet may adopt a permanent bouncing behavior, depending on both the forcing frequency and the forcing amplitude. The relationship between the droplet deformations and the bouncing mechanism is studied experimentally and theoretically through an asymmetric and dissipative bouncing spring model. Antiresonance effects are evidenced. Experiments and theoretical predictions show that both resonance at specific frequencies and antiresonance at Rayleigh frequencies play crucial roles in the bouncing mechanism. In particular, we show that they can be exploited for droplet size selection.Comment: 4 pages, 4 figures and 1 vide

Run Up of Surface and Internal Waves

The evolution of breaking waves propagating towards the shore and more specifically the run-up phase over the swash-zone for surface as well as for internal waves is considered. The study is based on a) laboratory run up experiments for surface waves ; b) laboratory stratified flow experiments and c) on field data describing the internal wave run up. The presentation is focused on the breaking and energy transfer mechanisms common to surface and internal waves in the swash-zone. The mathematical model taking into account turbulent mixing and dispersion effects is discussed

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

Exchange shift of stripe domains in antiferromagnetically coupled multilayers

Antiferromagnetically coupled multilayers with perpendicular anisotropy, as [CoPt]/Ru, Co/Ir, Fe/Au, display ferromagnetic stripe phases as the ground states. It is theoretically shown that the antiferromagnetic interlayer exchange causes a relative shift of domains in adjacent layers. This ``exchange shift'' is responsible for several recently observed effects: an anomalous broadening of domain walls, the formation of so-called ``tiger-tail'' patterns, and a ``mixed state'' of antiferromagnetic and ferromagnetic domains in [CoPt]/Ru multilayers. The derived analitical relations between the values of the shift and the strength of antiferromagnetic coupling provide an effective method for a quantitative determination of the interlayer exchange interactions.Comment: 4 pages, 3 figure