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Une approche formelle pour l'optimisation de systèmes à événements discrets

Juan Cardillo Albarran 1
1 LAAS-MOGISA
LAAS - Laboratoire d'analyse et d'architecture des systèmes
Abstract : This thesis is centered on optimization of discrete event dynamical systems over finite domains. Two basic optimization methods have been considered: the Minimum Principle and Dynamic Programming. The result of the approach based on the Minimum Principle has been established in the form of a Theorem in which the necessary optimality condition is defined in terms of a variational inequality separable with respect to stages. This inequality is an explicit function of control variables at the current time, of state variables and possibly exogenous parameters involved in the evolution model. A resolution technique for such a parametric variational inequality has been developed under a " min-max " type process, respectively for the current control and the other controls. A method of symbolic computation is proposed in the manuscript to optimize a polynomial form defined over a finite discrete set. The corresponding algorithm is denoted by the acronym SCDO (Symbolic Computation for Discrete Optimization). The outcome of the application of this algorithm to solving the above mentioned " Min-Max " problem is the expression of the symbolic control sequence in a symbolic form explicit in the system state (and the exogenous parameters). The approach based on Dynamic Programming directly exploits the parametric character and the decomposition framework of this method. Integration of the SCDO algorithm in both stages of the process (optimization and trajectory reconstruction) here again generates an expression of the optimal control sequence explicit in the state.
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Juan Cardillo Albarran. Une approche formelle pour l'optimisation de systèmes à événements discrets. Automatic. Université Paul Sabatier - Toulouse III, 2004. Español. ⟨tel-00010477⟩

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