Compositional abstraction and safety synthesis using overlapping symbolic models

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

Modeling and Feedback Control for Air Flow Regulation in Deep Pits

International audienceWe consider the problem of regulating the air quality in underground extraction rooms for mining industry. This is a challenging control problem where the flow dynamics, the interconnections between subsystems and the time-varying topology have to be taken into account along with real-time computation constraints. Our work is focused on the deep pit part of the ventilation system, which brings fresh air at a specified pressure to the extraction levels. The flow interactions and main automation elements are first presented, with a real-time engineering model of the complete mine ventilation system. A novel control-oriented model focused on the pressure dynamics is then introduced, as a convective-resistive partial differential equation (PDE) with multiple inputs where the time-varying transport coefficients are estimated based on the distributed measurements. A fast predictive controller (FPC) is finally proposed to compensate the pressure losses due to friction and multiple flow exhausts thanks to the ventilation pit input pressure regulation. Simulation results illustrate the efficiency of the modeling and control algorithms

A QSS approach for particle source identification in Tore Supra tokamak

International audienceIn this work, we consider the problem of particle source identification from distributed electron density measurements in fusion plasmas, such as the ones obtained in Tore Supra tokamak. A transport model, suitable for identification purposes, is first proposed based on a simplification of classical particle transport models. We then derive a quasi-steady state (QSS) description, which is shown to converge exponentially towards the true solution. Finally, an identification method is proposed based on the QSS model and a shape approximation of the source term. ToreSupra data is used to illustrate the different results with experimental measurements

The Initialization Of Basal Sliding Coefficients For Antarctica, A Lyapunov Based Approach

International audience— Models describing natural phenomena can depend on parameters that cannot be directly measured, hence the necessity to develop inverse techniques to determine them. The goal of this paper is to utilize such a technique to enable better initialization of ice sheet models for Antarctica. This will enable models to produce better forecasts as part of climate studies. The parameter of interest is the basal sliding coefficient, which characterizes the contact of the ice sheet with the bed underneath. A Lyapunov based approach is proposed to control the convergence of the 1D inhomogeneous transport model toward a feasible equilibrium matching the measurements. This method results in a new update law for the coefficient inversion. The results, which show an improved convergence toward the observed ice thickness, are compared with a currently used inverse method

Adaptive Space-Time Distributed Parameter and Input Estimation in Heat Transport with Unknown Bounds

International audienceIn this paper, we discuss on-line adaptive estimation of distributed diffusion and source term coefficients for a non-homogeneous linear parabolic partial differential equation describing heat transport. An estimator is defined in the infinite-dimensional framework having the system state and the parameters' estimate as its states. Our scheme allows to estimate spatially distributed and space-time distributed parameters. While the parameters convergence depends on the plant signal richness assumption, the state convergence is established using the Lyapunov approach. Since the estimator is infinite- dimensional, the b-splines Galerkin finite element method is used to implement it. In silico simulations are provided to illustrate the performance of the proposed approach

Controllability and invariance of monotone systems for robust ventilation automation in buildings

International audienceThe problem considered is the temperature control in a building equipped with UnderFloor Air Distribution (UFAD). Its 0-D model is derived from the energy and mass conservation in each room, and also presents discrete components to describe the disturbances from heat sources and doors opening. Using the monotonicity of this model, we can characterize two concepts of robust control, the Robust Controllability and the Robust Controlled Invariance introduced in this paper, and determine their limits for control design objectives. The validity of these results is then illustrated in a simulation of a two-room example

Safety control with performance guarantees of cooperative systems using compositional abstractions

International audienceIn this paper, the monotonicity property is exploited to obtain symbolic abstractions, in the sense of alternating simulation, of a class of nonlinear control systems subject to disturbances. Both a centralized and a compositional approaches are presented to obtain such abstractions, from which controllers are synthesized to satisfy safety specifications and optimize a performance criterion using a receding horizon approach. Performance guarantees on the trajectories of the controlled system can be obtained with both approaches. The controller synthesis and performance guarantees are illustrated and compared on the temperature regulation in a building

On the Intelligent Proportional Controller Applied to Linear Systems

We analyze in this paper the effect of the well known intelligent proportional controller on the stability of linear control systems. Inspired by the literature on neutral time delay systems and advanced type systems, we derive sufficient conditions on the order of the control system, under which, the used controller fails to achieve exponential stability. Furthermore, we obtain conditions, relating the system s and the control parameters, such that the closed-loop system is either unstable or not exponentially stable. After that, we provide cases where the intelligent proportional controller achieves exponential stability. The obtained results are illustrated via numerical simulations, and on an experimental benchmark that consists of an electronic throttle valve

D1-Input-to-State Stability of a Time-Varying Nonhomogeneous Diffusive Equation Subject to Boundary Disturbances

International audienceD1-Input-to-state stability (D1ISS) of a diffusive equation with Dirichlet boundary conditions is shown, in the L2-norm, with respect to boundary disturbances. In particular, the spatially distributed diffusion coefficients are allowed to be time-varying within a given set, without imposing any constraints on their rate of variation. Based on a strict Lyapunov function for the system with homogeneous boundary conditions, D1ISS inequalities are derived for the disturbed equation. A heuristic method used to numerically compute weighting functions is discussed. Numerical simulations are presented and discussed to illustrate the implementation of the theoretical results

Adaptive Distributed Parameter and Input Estimation in Plasma Tokamak Heat Transport

International audienceIn this paper, the adaptive estimation of spatially varying diffusion and source term coefficients for a linear parabolic partial differential equation describing tokamak plasma heat transport is considered. An estimator is defined in the infinite-dimensional framework having the system state and the parameters' estimate as its states. Our scheme allows to estimate constant, spatially distributed and spatio-temporally distributed parameters as well as input with known upper bounds in time. While the parameters convergence depends on the plant signal richness assumption, the state convergence is established using the Lyapunov approach. Since the estimator is infinite-dimensional, the Galerkin finite-dimensional technique is used to implement it. In silico simulations are provided to illustrate the performance of the proposed approach