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.I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.