Jr. Dorroh et G. Ferreyra, A MULTISTATE, MULTICONTROL PROBLEM WITH UNBOUNDED CONTROLS, SIAM journal on control and optimization, 32(5), 1994, pp. 1322-1331
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.