On Some Extremal Problems Associated with Motion in a Velocity Field

详细

The extremals of the Pontryagin maximum principle for problems related to motion in the velocity field are studied. Controls are continuous functions. It is shown that in the state space there exists a neighborhood of the final point through each point of which there passes a single extremal trajectory leading to the final point. It is also shown that if the trajectory of an extremal contains a point that another extremal with the same value of the functional passes through, then this point cuts off the nonoptimal part from the trajectory. It is proved that the remaining part leading to the final point is optimal.