Distribution-Like Hamiltonian Flows and Generalized Optimal Controls.

In regular optimal-control problems, Pontryagin's maximum principle specifies possible optimal solutions among trajectories of a Hamiltonian system. In this paper, we show how to extend this approach to singular linear-quadratic optimal-control problems that have only "generalized" optimal solutions. We define generalized Hamiltonian flows whose trajectories are distributions (generalized functions). We show that generalized Hamiltonian trajectories correspond to the generalized optimal solutions of the problem and obtain a geometric description of the generalized optimal synthesis for singular linear-quadratic problems. [ABSTRACT FROM AUTHOR]