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Approche probabiliste pour la commande orientée évènement des systèmes stochastiques à commutation

Abstract : Hybrid systems are dynamical systems, characterized by a dual behaviour, a continuousinteraction between a discrete and a continuous functioning part. The center ofour work is represented by a particular class of hybrid systems, more specific by thestochastic switching systems which we model using continuous time Markov chains anddifferential equations.The random behaviour of such systems requires a special command which adapts tothe arbitrary events that can completely change the evolution of the system. We chose anevent-based control policy which is triggered only when it’s necessary (on an unforeseenevent - for example when a threshold that is reached), and until certain functioningconditions are met (the system returns in the normal state).Our approach aims to develop a probabilistic model that calculates a performancecriterion (in this case the energy of the system) for the proposed control policy. We startby proposing a discrete event simulation for the controlled stochastic switching system,which gives us the opportunity of applying a direct optimisation of the control command.It also allows us to compare the results with the ones obtained by the analytical modelswe have built when the event-based control is applied.An analytical model for computing the energy consumed by the system to apply thecontrol is designed by using the exit probabilities of the control region, respectively, thesojourn times of the Markov chain before and after reaching the control limits. The lastpart of this work presents the results we have obtained when comparing the analyticaland the simulation method.
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Submitted on : Friday, January 4, 2013 - 11:41:34 PM
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  • HAL Id : tel-00770325, version 1



Adriana Mihaita. Approche probabiliste pour la commande orientée évènement des systèmes stochastiques à commutation. Autre. Université de Grenoble, 2012. Français. ⟨NNT : 2012GRENT036⟩. ⟨tel-00770325⟩



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