Bang--bang trajectories with a double switching time: sufficient strong local optimality conditions

TL;DR

This paper establishes sufficient conditions for the local optimality of bang-bang trajectories with multiple switches, extending previous results by incorporating second order conditions and strict Legendre conditions.

Contribution

It introduces generalized strong local optimality conditions for bang-bang extremals with multiple switches, including second order conditions for switching time variations.

Findings

Derived sufficient conditions for local optimality of bang-bang trajectories

Extended previous optimality conditions to multiple switch scenarios

Validated the conditions through theoretical analysis

Abstract

This paper gives sufficient conditions for a class of bang-bang extremals with multiple switches to be locally optimal in the strong topology. The conditions are the natural generalizations of the ones considered in previous papers for more specific cases. We require both the strict bang-bang Legendre condition, and the second order conditions for the finite dimensional problem obtained by moving the switching times of the reference trajectory.