General LQG Homing Problems in One Dimension

الملخص EN

Optimal control problems for one-dimensional diffusion processes in the interval (d1,d2) are considered.

The aim is either to maximize or to minimize the time spent by the controlled processes in (d1,d2).

Exact solutions are obtained when the processes are symmetrical with respect to d∗∈(d1,d2).

Approximate solutions are derived in the asymmetrical case.

The one-barrier cases are also treated.

Examples are presented.