Abstract
In Chap. 20 we established that the sign of the quadratic form λ t Hess ũ F t is related to optimality of the extremal control ũ. Under natural assumptions, the second variation is negative on short segments. Now we wish to catch the instant of time where this quadratic form fails to be negative. We derive an ODE (Jacobi equation) that allows to find such instants (conjugate times). Moreover, we give necessary and sufficient optimality conditions in these terms.
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© 2004 Springer-Verlag Berlin Heidelberg
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Agrachev, A.A., Sachkov, Y.L. (2004). Jacobi Equation. In: Control Theory from the Geometric Viewpoint. Encyclopaedia of Mathematical Sciences, vol 87. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-06404-7_21
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DOI: https://doi.org/10.1007/978-3-662-06404-7_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05907-0
Online ISBN: 978-3-662-06404-7
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