On Korobov's admissible maximum principle

Based on the controllability function method a family of bang-bang controls satisfying Korobov's admissible maximum principle (KAMP) for the Brunovsky control system is given. By using the resultant of two polynomials the switching surface corresponding to the Pontryagin maximum principle (PMP) as well as the KAMP for control system of dimension 2 are attained. A conjecture of switching surfaces of the PMP and KAMP for the Brunovsky system of dimension 3 is presented.