Abstract
For control systems of the form $\dot x = X(x) + \sum_{i = 1}^m {Y_i (x)u_i } $, 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.
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