Singularly Perturbed Hybrid Control Systems Approximated by Structured Linear Programs

The aim of this tutorial paper is to present the relationship that exists between the control of singularly perturbed hybrid stochastic systems and the decomposition approach in structured linear programs The mathematical sophistication is voluntarily kept at a low level byavoiding the full development of the theorems demonstrations that can be found in papers already published or to appear shortly. On another hand, since it corresponds to a new application of a convex optimization method that has been successfully applied in other contexts, we give a rather detailed account of the decomposition technique used in the numerical approximation method and of the comparison with a direct linear programming method.

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