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Necessary conditions of optimality for vector-valued impulsive control problems. (English) Zbl 0985.49023
Summary: A vector-valued impulsive control problem is considered whose dynamics, defined by a differential inclusion, are such that the vector fields associated with the singular term do not satisfy the so-called Frobenius condition. A concept of robust solution based on a new reparametrization procedure is adopted in order to derive necessary conditions of optimality. These conditions are obtained by taking a limit of those for an appropriate sequence of auxiliary “standard” optimal control problems approximating the original one. An example to illustrate the nature of the new optimality conditions is provided.

MSC:
49N25 Impulsive optimal control problems
49K24 Optimal control problems with differential inclusions (nec./ suff.) (MSC2000)
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