Conjugacy for normal or abnormal linear Bolza problems

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Abstract

For certain Bolza problems with linear dynamics, two sets extending the notion of conjugate points in the calculus of variations are introduced. Independently of nonsingularity assumptions, their emptiness, in one case without normality assumptions, is shown to be equivalent to a second order necessary condition. A comparison with other notions available in the literature is given.

Keywords

Optimal control
Conjugate points
Second order necessary conditions
Normality

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