A MULTISTATE, MULTICONTROL PROBLEM WITH UNBOUNDED CONTROLS

This paper gives the optimal synthesis for a two-dimensional singular control problem of the Vidale-Wolfe type. The controls take values in an unbounded set. Moreover, the optimal feedback control turns out to be impulsive on certain regions, and the order in which these impulses occur is important. A parameterization of time is introduced into the problem. This helps to elucidate the optimal synthesis, to prove its optimality by the verification method, and to design suboptimal physic al approximations to the optimal impulsive control.