HIGH ORDER TEST FOR OPTIMALITY OF BANG-BANG CONTROLS.

For control systems of the form dx/dt equals X(x) plus SIGMA Y//i(x)u//i, where the summation is from i equals l to m, a strengthened version of the classical Pontryagin maximum principle is proved. The necessary condition for optimality given here is obtained using functional analytic techniques and quite general high-order perturbations of the reference control. As shown by an example, this test is particularly effective when applied to bang-bang controls, a case where other high order tests do not provide additional information.