Structural stability without coercivity

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.

Keywords:

• Structural stability
• bang-bang-singular extremals
• Hamiltonian methods

Disclosure statement

No potential conflict of interest was reported by the author(s).