EXPONENTIAL CONVERGENCE TOWARDS CONSENSUS FOR NON-SYMMETRIC LINEAR FIRST-ORDER SYSTEMS IN FINITE AND INFINITE DIMENSIONS

We consider finite and infinite-dimensional first-order consensus systems with time-constant interaction coefficients. For symmetric coefficients, convergence to consensus is classically established by proving, for instance, that the usual variance is an exponentially decreasing Lyapunov function. We investigate here the convergence to consensus in the non-symmetric case: we identify a positive weight which allows us to define a weighted mean corresponding to the consensus and obtain exponential convergence towards consensus. Moreover, we compute the sharp exponential decay rate

An algorithmic guide for finite-dimensional optimal control problems

We survey the main numerical techniques for finite-dimensional nonlinear optimal control. The chapter is written as a guide to practitioners who wish to get rapidly acquainted with the main numerical methods used to efficiently solve an optimal control problem. We consider two classical examples, simple but significant enough to be enriched and generalized to other settings: Zermelo and Goddard problems. We provide sample of the codes used to solve them and make these codes available online. We discuss direct and indirect methods, Hamilton–Jacobi approach, ending with optimistic planning. The examples illustrate the pros and cons of each method, and we show how these approaches can be combined into powerful tools for the numerical solution of optimal control problems for ordinary differential equations

Protective walls against effects of vapor cloud fast deflagration CFD recommendations for design

International audienceProtective walls are a well-known and efficient way to mitigate overpressure effects of explosions. For detonation there are multiple published investigations concerning interactions of blast waves and walls, whereas for deflagration no well-adapted and rigorous method has been reported in the literature. This article describes the validation of a new computational fluid dynamics (CFD) modeling approach for fast deflagrations. In a first step, the vapor cloud explosion involving a fast deflagration is substituted by an equivalent vessel burst problem. The purpose of this step is to avoid reactive flow computations. In a second step, CFD is used to model the pressure propagation from the equivalent (nonreactive) vessel burst problem. After verifying the equivalence of the fast deflagration and the vessel burst problem in the first step, the ability of two CFD codes FLACS and Europlexus is examined for situations with and without barriers. Parametric analysis by means of numerical simulations is performed to investigate the efficiency of finite barriers to mitigate blast waves. Another parametric study shows how the maximum overpressure value in the shade of the barrier depends on the magnitude of the incoming overpressure wave. On this basis, several recommendations are suggested for designing protective walls. © 2017 American Institute of Chemical Engineers Process Process Saf Prog 3756–66, 2018. © 2017 American Institute of Chemical Engineer

A new method to assess mitigation efficiency of a protective barrier against the effects of a vapor cloud explosion

Accidental gas explosions represent an ever-present hazard for process industries handling flammable gases and liquids. There is also an increasing danger of vandals and terrorists using improvised explosive devices in industrial areas neighboring highly populated residential areas. The consecutive pressure wave generation and propagation can result in unacceptable risk exposition of citizens and infrastructures. Therefore, it is necessary to define design rules of protective barriers mitigating the effect of blast wave