Necessary conditions of optimality for vector-valued impulsive control problems.

*(English)*Zbl 0985.49023Summary: 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) |

##### Keywords:

vector-valued impulsive control; differential inclusions; necessary conditions for optimality
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\textit{F. L. Pereira} and \textit{G. N. Silva}, Syst. Control Lett. 40, No. 3, 205--215 (2000; Zbl 0985.49023)

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##### References:

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