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This chapter examines the biophysical, socio-economic, environmental and human health dimensions of urban and peri-urban agriculture in Dakar city (Senegal) and identifies structural threats to urban agriculture, including those already induced, or have the potential to be induced, by climate change. Urban agriculture, which provides an important source of fresh vegetables and other fresh products for the city is being increasingly marginalised due to a combination of factors including diminished soil and water quality, increasing temperatures and reduced rainfall, urban encroachment and pollution from industrial sources. A lack of clearly defined roles and responsibilities between local and national governments hinders the ability to protect urban agricultural land from urban encroachment and a lack of access to credit by farmers adds to their ability to cope with the multitude of other pressures. Dakar is bordered by the Atlantic Ocean on the northern, western and southern sides with no room for expansion, including any potential expansion of urban agriculture. Ground water in this urban zone is steadily deteriorating due to nitrate pollution of shallow groundwater in soil aquifers combined with increasing saltwater intrusion. Recycling of untreated wastewater for use in urban agriculture, a common practice in Dakar and other cities in Africa has increased the incidence of food-borne contamination. For example, recent microbial sampling of water showed a very high proportion of sites (87 %) with contamination levels above World Health Organisation standards for irrigation without restriction. Solid and liquid waste management is one of the biggest problems Dakar is facing as are many other cities of developing countries. Climate change will further impact urban agriculture. Shortening of cold periods favorable to vegetable cropping in semi-arid areas, increasingly hotter summers, more frequent flooding and drought periods, and higher incidence of pest and diseases are among the potential impacts of climate change. Coastal zones of the city are particularly under threat due to the rising sea level with negative consequences of coastal erosion and salt-water intrusion in lowlands. Projection models show a strong warming trend in the region. Conversely, there is no agreed trend of rainfall prediction at present but deficits are anticipated by general circulation models. Adaptation strategies of farmers include lifting the ground surface with landfill in order to better cope with flooding (specifically for flower cultivation), development of soil and soilless micro gardens in boxes, crop diversification and use of hybrid seeds. Urban agriculture has the potential to contribute to climate change adaptation through reinforcement of urban agricultural systems resilience, water recycling, buffering thermal and hydraulic shocks, providing safe and nutritious food, recycling wastes and conserving biodiversity. Despite its huge potential to reduce poverty and make the city more resilient to impacts from climate change, urban agriculture is not high on the urban planning agenda. Recommendations are formulated towards taking into consideration urban agriculture in national and local planning, strengthening capacities of stakeholders and awareness at all levels of society on the economic, social and environmental role of urban agriculture can play in sustainable development and greening of the city and its economy.

The aim of this paper is to present a new scaling which is appropriate for modeling reverse biased semiconductor devices with moderately high applied potential and its asymptotic analysis. This scaling was motivated by the modeling of oxygen sensors. It is compared to the ones leading to (a) electroneutrality, (b) the existence of a depletion zone. With our scaling such a zone may appear within a boundary layer. A particular attention is paid to the qualitative dependence of the asymptotic solution to the boundary value of the concentration of carrier.

This paper presents a method which aims at improving parameter estimation in dynamical systems. The general principle of the method is based on a modification of the least-squares objective function by means of a weighting operator, in view to improve the conditioning of the identification problem. First we recall a previous work using variational calculus in order to obtain the weighting operators through a linear equation. Then we propose a new approach which consists of determining the weights by formulating an optimization problem including positive semidefinite constraints (linear matrix inequalities, LMI). Copyright © 2001 John Wiley & Sons, Ltd.

Proper orthogonal decomposition (POD) is a Galerkin method which has been introduced in a fluids mechanics context. It is also known as Karhunen-Loeve decomposition and principal component analysis. The idea of POD consists in using a priori known information on the solution u of PDE, for example snapshots u i = u(t i), to determine a set of functions which are the eigenfunctions of an Hilbert-Schmidt operator. This basis can be used to solve the PDE with a smaller amount of computations. Convergence estimates have been proved recently in the parabolic case starting from a particular discretization scheme [7]. Moreover it has been proved that the method converges independently from the scheme [6]. We consider the case of a linear parabolic equation. We give a first convergence estimate in a case where u is regular. However classical POD does not look satisfactory and an improvement consists in considering a POD which takes into account the derivative of u. We will also present some insights into the control of the approximation by introducing what will be called a good order of approximation.

We study the problem of designing a feedback controller for wave generators in a canal. The goal is to obtain a progressive wave at the surface by acting on plane generators at each side of a rectangular canal. The model of such a system is given by a classical linear model of shallow waters which leads to an hyperbolic equation. We formulate the problem within the additive uncertainty framework for Callier-Desoer systems and we use the standard algorithm of Doyle et al. to obtain a finite dimensional controller that ensures robust stability of the closed loop system and a prespecified performance level in a narrow frequency band. Numerical results show that we are able to create and maintain a progressive wave on the surface of the canal with this controller. We also give as a benchmark numerical and experimental results on the open loop approach of this problem.

We study the problem of designing a feedback controller for wave generators in a canal. The goal is to obtain a progressive wave at the surface by acting on plane generators at each side of a rectangular canal. The model of such a system is given by a classical linear model of shallow waters which leads to a damped „hyperbolic” equation. We formulate the problem within the additive uncertainty framework for Callier-Desoer systems and we then use the standard algorithm of Doyle and al. to derive a finite dimensional controller that ensures robust stability of the closed loop system and a prespecified performance level in a narrow frequency band. Numerical results show that we are able to create and maintain a progressive wave on the surface of the canal with this controller. We also show that the closed loop system remains stable with variations of the damping parameter.

Optimal control problems for systems governed by partial differential equations are now solved currently. Restricting ourselves to open loop controls, the techniques used are essentially adaptations of those used for the control of lumped systems. Most successful of all is the gradient method although quasi Newton and conjugate gradient methods could be used ; however the selection of an efficient step size rule is more than ever crucial. The evaluation of the cost function is so expensive that the search for a one dimensional minimum must be avoided. Linear instantaneous constraints on the control and/or the states variables can be handled by the gradient projection method and/or duality or penalization.

A hot strip rolling mill is a complex system which requires sophisticated regulations in order to obtain a constant thickness of the strip at the exit of the mill (the screw positions and the roll speeds are the control variables). Here we present new regulations which take in account the temperature measurements at the exit of the roughing mill. The preset values of the control variables are computed before the milling (feed-forward) These values are modified during the milling by a feedback based upon the forces measurements. This type of system which has the same structure as an Automatic Gauge Control (AGC) is easy to implement on the process.