Internal model control of nonlinear systems through the inversion of recurrent neural networks

Recurrent neural networks can be used for both the identification and control of nonlinear systems. This paper takes a previously derived set of theoretical results about recurrent neural networks and applies them to the task of providing internal model control for a nonlinear plant. Using the theoretical results, we show how an inverse controller can be produced from a neural network model of the plant, without the need to train an additional network to perform the inverse control.

Bifurcation Analysis of Eigenstructure Assignment Control in a Simple Nonlinear Aircraft Model

Aircraft systems are highly nonlinear and time varying. High-performance aircraft at high angles of incidence experience undesired coupling of the lateral and longitudinal variables, resulting in departure from normal controlled � ight. The construction of a robust closed-loop control that extends the stable and decoupled � ight envelope as far as possible is pursued. For the study of these systems, nonlinear analysis methods are needed. Previously, bifurcation techniques have been used mainly to analyze open-loop nonlinear aircraft models and to investigate control effects on dynamic behavior. Linear feedback control designs constructed by eigenstructure assignment methods at a � xed � ight condition are investigated for a simple nonlinear aircraft model. Bifurcation analysis, in conjunction with linear control design methods, is shown to aid control law design for the nonlinear system.

Applying robust control theory to solve problems in bio-medical sciences: study of an apoptotic model

Biological models of an apoptotic process are studied using models describing a system of differential equations derived from reaction kinetics information. The mathematical model is re-formulated in a state-space robust control theory framework where parametric and dynamic uncertainty can be modelled to account for variations naturally occurring in biological processes. We propose to handle the nonlinearities using neural networks.

Evaluating the century C model using long-term fertilizer trials in the Indo-Gangetic Plains, India

The GEFSOC Project developed a system for estimating soil carbon (C) stocks and changes at the national and sub-national scale. As part of the development of the system, the Century ecosystem model was evaluated for its ability to simulate soil organic C (SOC) changes in environmental conditions in the Indo-Gangetic Plains, India (IGP). Two long-term fertilizer trials (LTFT), with all necessary parameters needed to run Century, were used for this purpose: a jute (Corchorus capsularis L.), rice (Oryza sativa L.) and wheat (Triticum aestivum L.) trial at Barrackpore, West Bengal, and a rice-wheat trial at Ludhiana, Punjab. The trials represent two contrasting climates of the IGP, viz. semi-arid, dry with mean annual rainfall (MAR) of < 800 mm and humid with > 1600 turn. Both trials involved several different treatments with different organic and inorganic fertilizer inputs. In general, the model tended to overestimate treatment effects by approximately 15%. At the semi-arid site, modelled data simulated actual data reasonably well for all treatments, with the control and chemical N + farm yard manure showing the best agreement (RMSE = 7). At the humid site, Century performed less well. This could have been due to a range of factors including site history. During the study, Century was calibrated to simulate crop yields for the two sites considered using data from across the Indian IGP. However, further adjustments may improve model performance at these sites and others in the IGP. The availability of more longterm experimental data sets (especially those involving flooded lowland rice and triple cropping systems from the IGP) for testing and validation is critical to the application of the model's predictive capabilities for this area of the Indian sub-continent. (C) 2007 Elsevier B.V. All rights reserved.

Modeling the mechanisms that control in-stream dissolved organic carbon dynamics in upland and forested catchments

[1] We present a new, process-based model of soil and stream water dissolved organic carbon (DOC): the Integrated Catchments Model for Carbon (INCA-C). INCA-C is the first model of DOC cycling to explicitly include effects of different land cover types, hydrological flow paths, in-soil carbon biogeochemistry, and surface water processes on in-stream DOC concentrations. It can be calibrated using only routinely available monitoring data. INCA-C simulates daily DOC concentrations over a period of years to decades. Sources, sinks, and transformation of solid and dissolved organic carbon in peat and forest soils, wetlands, and streams as well as organic carbon mineralization in stream waters are modeled. INCA-C is designed to be applied to natural and seminatural forested and peat-dominated catchments in boreal and temperate regions. Simulations at two forested catchments showed that seasonal and interannual patterns of DOC concentration could be modeled using climate-related parameters alone. A sensitivity analysis showed that model predictions were dependent on the mass of organic carbon in the soil and that in-soil process rates were dependent on soil moisture status. Sensitive rate coefficients in the model included those for organic carbon sorption and desorption and DOC mineralization in the soil. The model was also sensitive to the amount of litter fall. Our results show the importance of climate variability in controlling surface water DOC concentrations and suggest the need for further research on the mechanisms controlling production and consumption of DOC in soils.

Eutrophication control in river-systems: an application of INCA-P to the River Lugg

The Integrated Catchments model of Phosphorus dynamics (INCA-P) was applied to the River Lugg to determine the key factors controlling delivery of phosphorus to the main channel and to quantify the relative contribution of diffuse and point sources to the in-stream phosphorus (P) load under varying hydrological conditions. The model is able to simulate the seasonal variations and inter-annual variations in the in-stream total-phosphorus concentrations. However, difficulties in simulating diffuse inputs arise due to equifinality in the model structure and parameters. The River Lugg is split into upper and lower reaches. The upper reaches are dominated by grassland and woodland, so the patterns in the stream-water total-phosphorus concentrations are typical of diffuse source inputs; application of the model leads to estimates of the relative contribution to the in-stream P load from diffuse and point sources as 9:1. In the lower reaches, which are more intensively cultivated and urbanised, the stream-water total-phosphorus concentration dynamics are influenced more by point-sources; the simulated relative diffuse/point contribution to the in-stream P load is 1: 1. The model set-up and simulations are used to identify the key source-areas of P in the catchment, the P contribution of the Lugg to the River Wye during years with contrasting precipitation inputs, and the uptake and release of P from within-reach sediment. In addition, model scenarios are run to identify the impacts of likely P reductions at sewage treatment works on the in-stream soluble-reactive P concentrations and the suitability of this as a management option is assessed for reducing eutrophication.

Bjerknes compensation and the decadal variability of the energy transports in a coupled climate model

In the 1960s, Jacob Bjerknes suggested that if the top-of-the-atmosphere (TOA) fluxes and the oceanic heat storage did not vary too much, then the total energy transport by the climate system would not vary too much either. This implies that any large anomalies of oceanic and atmospheric energy transport should be equal and opposite. This simple scenario has become known as Bjerknes compensation. A long control run of the Third Hadley Centre Coupled Ocean-Atmosphere General Circulation Model (HadCM3) has been investigated. It was found that northern extratropical decadal anomalies of atmospheric and oceanic energy transports are significantly anticorrelated and have similar magnitudes, which is consistent with the predictions of Bjerknes compensation. ne degree of compensation in the northern extratropics was found to increase with increasing, time scale. Bjerknes compensation did not occur in the Tropics, primarily as large changes in the surface fluxes were associated with large changes in the TOA fluxes. In the ocean, the decadal variability of the energy transport is associated with fluctuations in the meridional overturning circulation in the Atlantic Ocean. A stronger Atlantic Ocean energy transport leads to strong warming of surface temperatures in the Greenland-Iceland-Norwegian (GIN) Seas. which results in a reduced equator-to-pole surface temperature gradient and reduced atmospheric baroclinicity. It is argued that a stronger Atlantic Ocean energy transport leads to a weakened atmospheric transient energy transport.

North Atlantic Oscillation response to transient greenhouse gas forcing and the impact on European winter climate: a CMIP2 multi-model assessment

This study investigates the response of wintertime North Atlantic Oscillation (NAO) to increasing concentrations of atmospheric carbon dioxide (CO2) as simulated by 18 global coupled general circulation models that participated in phase 2 of the Coupled Model Intercomparison Project (CMIP2). NAO has been assessed in control and transient 80-year simulations produced by each model under constant forcing, and 1% per year increasing concentrations of CO2, respectively. Although generally able to simulate the main features of NAO, the majority of models overestimate the observed mean wintertime NAO index of 8 hPa by 5-10 hPa. Furthermore, none of the models, in either the control or perturbed simulations, are able to reproduce decadal trends as strong as that seen in the observed NAO index from 1970-1995. Of the 15 models able to simulate the NAO pressure dipole, 13 predict a positive increase in NAO with increasing CO2 concentrations. The magnitude of the response is generally small and highly model-dependent, which leads to large uncertainty in multi-model estimates such as the median estimate of 0.0061 +/- 0.0036 hPa per %CO2. Although an increase of 0.61 hPa in NAO for a doubling in CO2 represents only a relatively small shift of 0.18 standard deviations in the probability distribution of winter mean NAO, this can cause large relative increases in the probabilities of extreme values of NAO associated with damaging impacts. Despite the large differences in NAO responses, the models robustly predict similar statistically significant changes in winter mean temperature (warmer over most of Europe) and precipitation (an increase over Northern Europe). Although these changes present a pattern similar to that expected due to an increase in the NAO index, linear regression is used to show that the response is much greater than can be attributed to small increases in NAO. NAO trends are not the key contributor to model-predicted climate change in wintertime mean temperature and precipitation over Europe and the Mediterranean region. However, the models' inability to capture the observed decadal variability in NAO might also signify a major deficiency in their ability to simulate the NAO-related responses to climate change.

El Nino-mean state-seasonal cycle interactions in a multi-model ensemble

The modelled El Nino-mean state-seasonal cycle interactions in 23 coupled ocean-atmosphere GCMs, including the recent IPCC AR4 models, are assessed and compared to observations and theory. The models show a clear improvement over previous generations in simulating the tropical Pacific climatology. Systematic biases still include too strong mean and seasonal cycle of trade winds. El Nino amplitude is shown to be an inverse function of the mean trade winds in agreement with the observed shift of 1976 and with theoretical studies. El Nino amplitude is further shown to be an inverse function of the relative strength of the seasonal cycle. When most of the energy is within the seasonal cycle, little is left for inter-annual signals and vice versa. An interannual coupling strength (ICS) is defined and its relation with the modelled El Nino frequency is compared to that predicted by theoretical models. An assessment of the modelled El Nino in term of SST mode (S-mode) or thermocline mode (T-mode) shows that most models are locked into a S-mode and that only a few models exhibit a hybrid mode, like in observations. It is concluded that several basic El Nino-mean state-seasonal cycle relationships proposed by either theory or analysis of observations seem to be reproduced by CGCMs. This is especially true for the amplitude of El Nino and is less clear for its frequency. Most of these relationships, first established for the pre-industrial control simulations, hold for the double and quadruple CO2 stabilized scenarios. The models that exhibit the largest El Nino amplitude change in these greenhouse gas (GHG) increase scenarios are those that exhibit a mode change towards a T-mode (either from S-mode to hybrid or hybrid to T-mode). This follows the observed 1976 climate shift in the tropical Pacific, and supports the-still debated-finding of studies that associated this shift to increased GHGs. In many respects, these models are also among those that best simulate the tropical Pacific climatology (ECHAM5/MPI-OM, GFDL-CM2.0, GFDL-CM2.1, MRI-CGM2.3.2, UKMO-HadCM3). Results from this large subset of models suggest the likelihood of increased El Nino amplitude in a warmer climate, though there is considerable spread of El Nino behaviour among the models and the changes in the subsurface thermocline properties that may be important for El Nino change could not be assessed. There are no clear indications of an El Nino frequency change with increased GHG.

ENSO at 6ka and 21ka from ocean–atmosphere coupled model simulations

We analyze how the characteristics of El Niño-Southern Oscillation (ENSO) are changed in coupled ocean–atmosphere simulations of the mid-Holocene (MH) and the Last Glacial Maximum (LGM) performed as part of the Paleoclimate Modeling Intercomparison Project phase 2 (PMIP2). Comparison of the model results with present day observations show that most of the models reproduce the large scale features of the tropical Pacific like the SST gradient, the mean SST and the mean seasonal cycles. All models simulate the ENSO variability, although with different skill. Our analyses show that several relationships between El Niño amplitude and the mean state across the different control simulations are still valid for simulations of the MH and the LGM. Results for the MH show a consistent El Niño amplitude decrease. It can be related to the large scale atmospheric circulation changes. While the Northern Hemisphere receives more insolation during the summer time, the Asian summer monsoon system is strengthened which leads to the enhancement of the Walker circulation. Easterlies prevailing over the central eastern Pacific induce an equatorial upwelling that damps the El Niño development. Results are less conclusive for 21ka. Large scale dynamic competes with changes in local heat fluxes, so that model shows a wide range of responses, as it is the case in future climate projections.

Stratospheric water vapour and high climate sensitivity in a version of the HadSM3 climate model

It has been shown previously that one member of the Met Office Hadley Centre single-parameter perturbed physics ensemble – the so-called "low entrainment parameter" member – has a much higher climate sensitivity than other individual parameter perturbations. Here we show that the concentration of stratospheric water vapour in this member is over three times higher than observations, and, more importantly for climate sensitivity, increases significantly when climate warms. The large surface temperature response of this ensemble member is more consistent with stratospheric humidity change, rather than upper tropospheric clouds as has been previously suggested. The direct relationship between the bias in the control state (elevated stratospheric humidity) and the cause of the high climate sensitivity (a further increase in stratospheric humidity) lends further doubt as to the realism of this particular integration. This, together with other evidence, lowers the likelihood that the climate system's physical sensitivity is significantly higher than the likely upper range quoted in the Intergovernmental Panel on Climate Change's Fourth Assessment Report.

Estimating the hidden number of scrapie affected holdings in great Britain using a simple, truncated count model allowing for heterogeneity.

None of the current surveillance streams monitoring the presence of scrapie in Great Britain provide a comprehensive and unbiased estimate of the prevalence of the disease at the holding level. Previous work to estimate the under-ascertainment adjusted prevalence of scrapie in Great Britain applied multiple-list capture–recapture methods. The enforcement of new control measures on scrapie-affected holdings in 2004 has stopped the overlapping between surveillance sources and, hence, the application of multiple-list capture–recapture models. Alternative methods, still under the capture–recapture methodology, relying on repeated entries in one single list have been suggested in these situations. In this article, we apply one-list capture–recapture approaches to data held on the Scrapie Notifications Database to estimate the undetected population of scrapie-affected holdings with clinical disease in Great Britain for the years 2002, 2003, and 2004. For doing so, we develop a new diagnostic tool for indication of heterogeneity as well as a new understanding of the Zelterman and Chao’s lower bound estimators to account for potential unobserved heterogeneity. We demonstrate that the Zelterman estimator can be viewed as a maximum likelihood estimator for a special, locally truncated Poisson likelihood equivalent to a binomial likelihood. This understanding allows the extension of the Zelterman approach by means of logistic regression to include observed heterogeneity in the form of covariates—in case studied here, the holding size and country of origin. Our results confirm the presence of substantial unobserved heterogeneity supporting the application of our two estimators. The total scrapie-affected holding population in Great Britain is around 300 holdings per year. None of the covariates appear to inform the model significantly.