We study structural stability and local uniqueness of bang-bang-singular extremals in a fixed-free Mayer problem. The problem can be seen as an optimal control problem where the dynamics is control-affine. We prove our results under the same assumptions on the nominal problem that permit us to prove that the extremal is a strict strong local optimiser: suitable regularity assumptions and coercivity of a restriction of the {em extended second variation}. We also assume that the condition that prevents the coercivity of the extended second variation is stable with respect to the parameter.

Structural stability without coercivity / Poggiolini Laura; Stefani Gianna. - In: OPTIMIZATION. - ISSN 0233-1934. - STAMPA. - 71:(2022), pp. 3327-3350. [10.1080/02331934.2022.2032696]

Structural stability without coercivity

Poggiolini Laura
;
Stefani Gianna
2022

Abstract

We study structural stability and local uniqueness of bang-bang-singular extremals in a fixed-free Mayer problem. The problem can be seen as an optimal control problem where the dynamics is control-affine. We prove our results under the same assumptions on the nominal problem that permit us to prove that the extremal is a strict strong local optimiser: suitable regularity assumptions and coercivity of a restriction of the {em extended second variation}. We also assume that the condition that prevents the coercivity of the extended second variation is stable with respect to the parameter.
71
3327
3350
Poggiolini Laura; Stefani Gianna
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2158/1253712
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