Abstract
We investigate a long-run behavior of a linear stochastic system. It is assumed that the quadratic cost includes a time-varying function and its multiplicative inverse. Such a specification reflects the fact that time preferences used by agents to assess different types of losses evolve in opposite directions. We consider the case when priority is set for the losses associated with state deviations. The optimal control law is derived with respect to extended long-run average cost criteria. We provide conditions for the existence of an alternative control strategy, which is also optimal and is based on a solution of an algebraic Riccati equation.
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