Optimal control of a class of discrete–continuous non-linear systems — decomposition and hierarchical structure

A technique is derived for solving a non-linear optimal control problem by iterating on a sequence of simplified problems in linear quadratic form. The technique is designed to achieve the correct solution of the original non-linear optimal control problem in spite of these simplifications. A mixed approach with a discrete performance index and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local sub-system problems and a co-ordinator within a hierarchical framework. An analysis of the optimality and convergence properties of the algorithm is presented and the effectiveness of the technique is demonstrated using a simulation example with a non-separable performance index.

Asymmetric forcing from stratospheric aerosols impacts Sahelian rainfall

The Sahelian drought of the 1970s–1990s was one of the largest humanitarian disasters of the past 50 years, causing up to 250,000 deaths and creating 10 million refugees1. It has been attributed to natural variability2–5, overgrazing6 and the impact of industrial emissions of sulphur dioxide7,8. Each mechanism can influence the Atlantic sea surface temperature gradient, which is strongly coupled to Sahelian precipitation2,3. We suggest that sporadic volcanic eruptions in the Northern Hemisphere also strongly influence this gradient and cause Sahelian drought. Using de-trended observations from 1900 to 2010, we show that three of the four driest Sahelian summers were preceded by substantial Northern Hemisphere volcanic eruptions. We use a state-ofthe- art coupled global atmosphere–ocean model to simulate both episodic volcanic eruptions and geoengineering by continuous deliberate injection into the stratosphere. In either case, large asymmetric stratospheric aerosol loadings concentrated in the Northern Hemisphere are a harbinger of Sahelian drought whereas those concentrated in the Southern Hemisphere induce a greening of the Sahel. Further studies of the detailed regional impacts on the Sahel and other vulnerable areas are required to inform policymakers in developing careful consensual global governance before any practical solar radiation management geoengineering scheme is implemented.

The carbon dioxide production rate assumption biases gastric emptying parameters in healthy adults

RATIONALE: An altered gastric emptying (GE) rate has been implicated in the aetiology of obesity. The (13)C-octanoic acid breath test (OBT) is frequently used to measure GE, and the cumulative percentage of (13)C recovered (cPDR) is a common outcome measure. However, true cPDR in breath is dependent on accurate measurement of carbon dioxide production rate (VCO(2)). The current study aimed to quantify differences in the (13)C OBT results obtained using directly measured VCO(2) (VCO(2DM)) compared with (i) predicted from resting VCO(2) (VCO(2PR)) and (ii) predicted from body surface area VCO(2) (VCO(2BSA)). METHODS: The GE rate of a high-fat test meal was assessed in 27 lean subjects using the OBT. Breath samples were gathered during the fasted state and at regular intervals throughout the 6-h postprandial period for determination of (13)C-isotopic enrichment by continuous-flow isotope-ratio mass spectrometry. The VCO(2) was measured directly from exhaled air samples and the PDR calculated by three methods. The bias and the limits of agreement were calculated using Bland-Altman plots. RESULTS: Compared with the VCO(2DM), the cPDR was underestimated by VCO(2PR) (4.8%; p = 0.0001) and VCO(2BSA) (2.7%; p = 0.02). The GE T(half) was underestimated by VCO(2PR) (13 min; p = 0.0001) and VCO(2BSA) (10 min; p = 0.01), compared with VCO(2DM). CONCLUSIONS: The findings highlight the importance of directly measuring VCO(2)production rates throughout the (13)C OBT and could partly explain the conflicting evidence regarding the effect of obesity on GE rates.