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Sufficient optimality conditions for a bang-singular extremal in the minimum time problem. (English) Zbl 1235.49054

Summary: The paper gives second order sufficient conditions for the strong local optimality of a bang-singular extremal in a minimum time problem. The conditions are given in terms of regularity assumptions on the extremal and of the coercivity of the extended second variation associated to the minimum time problem with fixed end-points on the singular arc. The conditions are close to the necessary ones in the usual sense, namely we require strict inequalities where necessary conditions have mild inequalities.

MSC:

49K30 Optimality conditions for solutions belonging to restricted classes (Lipschitz controls, bang-bang controls, etc.)
49K15 Optimality conditions for problems involving ordinary differential equations
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