Structural stability without coercivity. (2nd November 2022)

• Record Type: Journal Article
• Authors: Poggiolini, Laura; Stefani, Gianna
• Is Part Of: Optimization. Volume 71:Number 11(2022)
• Page Start: 3327
• Page End: 3350
• Publication Date: 2022-11-02
• Subjects: Structural stability -- bang-bang-singular extremals -- Hamiltonian methods; Mathematical optimization -- Periodicals; 519.7
• DOI: 10.1080/02331934.2022.2032696
• Languages: English
• ISSNs: 0233-1934

Abstract

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 optimizer: suitable regularity assumptions and coercivity of a restriction of the 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.