«Truncation» as a method for parametrization and solution of stochastic problems in control of optimal random duration

For design of optimal control strategies in a stochastic system given on a random time interval a control duration «truncation» is used. The «truncation» parameter $T$ dictates the control process duration. The boundary of the region of optimal random stoppages can be found by optimization of $T$ in associated Bellman functions. For a linear control system and a quadratic performance functional an explicit expression of the stoppage region boundary is obtained.