On the sufficiency of Pontryagin's maximum principle

Abstract

This work focus on sufficient conditions of optimality for an optimal control problem. A refined maximum principle condition which guarantees weak local optimality of control processes for affine control systems with a polyhedral set of controls is introduced. This refined maximum principle condition expresses that the control is uniquely de- fined for almost all instants of time and the behavior of adjoint variables is rather regular. Several examples are presented to illustrate such suf- ficient condition.