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Theory of singularities of the input/output function and optimality of singular trajectories in problems of minimal time. (Théorie des singularités de l’application entrée/sortie et optimalité des trajectoires singulières dans le problème du temps minimal.) (French) Zbl 0779.49025
Summary: We study the time optimality status of singular trajectories for single- input affine systems. The basic tools are the construction of semi-normal forms under the action of the transformation group generated by changes of coordinates and feedbacks and the use of an adapted representation of the input space, without allowing the evaluation of the accessibility sets. We get necessary and sufficient optimality conditions under generic or codimension one assumptions.

MSC:
49K15 Optimality conditions for problems involving ordinary differential equations
93C10 Nonlinear systems in control theory
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