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1

Optimal and Suboptimal Control of a Standard Brownian Motion

Lefebvre M.

Archives of Control Sciences

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2016

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Vol. 26, no. 3

383--394

EN

The problem of optimally controlling a standard Brownian motion until a fixed final time is considered in the case when the final cost function is an even function. Two particular problems are solved explicitly. Moreover, the best constant control as well as the best linear control are also obtained in these two particular cases.

2

Influence of the Shape of an Explosive Charge: Quantification of the Modification of the Pressure Field

Simoens B., Lefebvre M.

Central European Journal of Energetic Materials

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2015

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Vol. 12, no. 2

195--213

EN

Many scientific articles dealing with the detonation of explosive charges and their effects suppose that the charge is spherical and centrally initiated. Yet, when discussing the blast wave effect, the charge shape and the location of initiation could be as important as the composition or the mass of the considered explosive. Specifically, close to the charge, the shape may cause significant modifications of the pressure field compared to the predictions developed for spherical charges. Experiments have been carried out, using an emulsion explosive, TNT and C4, in order to quantify the shape effect. Unconfined, centrally initiated spherical and cylindrical charges with different length-to-diameter (L/D) ratios have been fired. The pressure in the median plane was recorded for different reduced distances. Results for spherical charges showed excellent agreement with well-known references. The expected change of the pressure field in the median plane of a cylindrical charge was observed, directly linked to the L/D ratio. Peak overpressure magnifications of up to almost 3 have been measured. The dimensions of the zone within which an increase of the blast wave effect is observed, have also been determined. A similar behaviour for TNT and C4 has been demonstrated; but a different behaviour has been observed for the emulsion explosive.

3

Ethylene Glycol Dinitrate (EGDN): from Commercial Precursors, Physicochemical and Detonation Characterization

Fettaka H., Lefebvre M.

Central European Journal of Energetic Materials

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2015

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Vol. 12, no. 2

287--305

EN

Currently, liquid explosives pose a potential threat. An important phase in the assessment of this threat is to investigate the various synthesis paths leading to their manufacture and to evaluate the potential use of readily purchasable precursors. The aim of this work was to assess the synthesis of Ethylene Glycol Dinitrate (EGDN), a liquid nitrate ester explosive, using commercially available precursors. The characteristics of the synthetic process (ease, yield), the chemical properties of the synthesized product (purity, spectra) and its explosive properties (sensitivities, detonability) were investigated. Comparisons are drawn between these products and the product obtained using laboratory ingredients. Three ingredients have been used: 1) ethylene glycol, laboratory grade, 2) ready to use, commercial coolant fluid, and 3) ethylene glycol extracted from commercial coolant fluid. The chemical composition and purity of the synthesized liquid explosive was analyzed by Gas Chromatography-Mass Spectrometry (GCMS), and infrared spectroscopy (IR). Differential Scanning Calorimetric (DSC) analysis allowed the heat of decomposition and activation energies to be assessed. The Ozawa and Kissinger models were used. The explosive properties of the pure synthesized products and comparable other explosives, have been tested. The potential use as a priming charge or as a main charge was assessed.

4

Discrete homing problems

Lefebvre M., Kounta M

Archives of Control Sciences

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2013

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Vol. 23, no. 1

5-18

EN

We consider the so-called homing problem for discrete-time Markov chains. The aim is to optimally control the Markov chain until it hits a given boundary. Depending on a parameter in the cost function, the optimizer either wants to maximize or minimize the time spent by the controlled process in the continuation region. Particular problems are considered and solved explicitly. Both the optimal control and the value function are obtained.

5

Probabilistic solution to a two-dimensional LQG homing problem

Makasu C., Lefebvre M.

Control and Cybernetics

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2012

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Vol. 41, no. 1

5-12

EN

Let xt be an arbitrary one-dimensional diffusion process and yt be a one-dimensional controlled diffusion process starting from y0 = y ∈ (a, b). The process is controlled until yt crosses either y = a or y = b for the first time. Our aim is to find the control ut that minimizes an expected cost functional with both quadratic control and boundary crossing costs. An explicit form for the optimal control is obtained under certain conditions.