The Effects of Discounted Cost on the Uncertainty Threshold Principle.

摘要

The optimal stochastic control of a linear system with purely random parameters and with respect to a discounted quadratic index of performance is considered. It is shown that if a function involving the parameter variances and the discount factor exceeds a certain threshold,then the infinite horizon optimization problem has no solution. On the other hand,it is also shown that the existence of optimal infinite horizon rules may not guarantee the stochastic stability of the underlying feedback system.