A sufficient optimality condition for piecewise C/sup 1/ extremal controls

We give an exposition of a few aspects of our methodology for the general nonlinear optimal control in the piecewise C/sup 1/ case. We obtain a sufficient optimality condition for piecewise C/sup 1/ extremal controls by a first order partial differential equation, an optimization process and the Pontryagin principle. We express the optimal value function by Lie series. Finally, we present the application of this method in singular optimal control problems.