In this paper, we develop a compositional approach to abstraction and safety synthesis for a general class of discrete time nonlinear systems. Our approach makes it possible to define a symbolic abstraction by composing a set of symbolic subsystems that are overlapping in the sense that they can share some common state variables. We develop compositional safety synthesis techniques using such overlapping symbolic subsystems. Comparisons, in terms of conservativeness and of computational complexity, between abstractions and controllers obtained from different system decompositions are provided. Numerical experiments show that the proposed approach for symbolic control synthesis enables a significant complexity reduction with respect to the centralized approach, while reducing the conservatism with respect to compositional approaches using non-overlapping subsystems.

Insoluble trace gases are trapped in polar ice at the firn-ice transition, at approximately 50 to 100 m below the surface, depending primarily on the site temperature and snow accumulation. Models of trace gas transport in polar firn are used to relate firn air and ice core records of trace gases to their atmospheric history. We propose a new model based on the following contributions. First, the firn air transport model is revised in a poromechanics framework with emphasis on the non-homogeneous properties and the treatment of gravitational settling. We then derive a nonlinear least square multi-gas optimisation scheme to calculate the effective firn diffusivity (automatic diffusivity tuning). The improvements gained by the multi-gas approach are investigated (up to ten gases for a single site are included in the optimisation process). We apply the model to four Arctic (Devon Island, NEEM, North GRIP, Summit) and seven Antarctic (DE08, Berkner Island, Siple Dome, Dronning Maud Land, South Pole, Dome C, Vostok) sites and calculate their respective depth-dependent diffusivity profiles. Among these different sites, a relationship is inferred between the snow accumulation rate and an increasing thickness of the lock-in zone defined from the isotopic composition of molecular nitrogen in firn air (denoted δ¹⁵N). It is associated with a reduced diffusivity value and an increased ratio of advective to diffusive flux in deep firn, which is particularly important at high accumulation rate sites. This has implications for the understanding of δ¹⁵N of N₂ records in ice cores, in relation with past variations of the snow accumulation rate. As the snow accumulation rate is clearly a primary control on the thickness of the lock-in zone, our new approach that allows for the estimation of the lock-in zone width as a function of accumulation may lead to a better constraint on the age difference between the ice and entrapped gases.

This paper describes a new industrial case on automation, for large‐scale systems with high environmental impact: the mining ventilation control systems. Ventilation control is essential for the operation of a mine in terms of safety (CO and NO_x regulation) and energy optimization. We first discuss a novel regulation architecture, highlighting the interest for a model‐based control approach and the use of distributed sensing capabilities thanks to a wireless sensor network (WSN). We propose a new model for underground ventilation. The main components of the system dynamics are described with time‐delays, transmission errors, energy losses and concentration profiles. Two different model‐based control approaches, which can embody the complex dynamics of the system, are proposed. The first one resorts to a nonlinear model predictive control strategy (receding horizon) and aims to energy minimization, thanks to a continuous operation of the fans. The second one, based on a hybrid description of the model and fans operation, provides automatic verification of the wireless control thanks to abstraction techniques. These control strategies are compared with simulations, in terms of regulation efficiency, energy consumption and the need for computational capabilities. The industrial case description and control strategies open new vistas for the development of global system approaches that allow for the optimization of energy consumption of complex large‐scale systems. Copyright © 2009 John Wiley & Sons, Ltd.