Geodesic
Optimal linear-quadratic regulator for a~stochastic system under mutually inverse time preferences in the cost
Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 1, pp. 38-56

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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.
Keywords: linear regulator of a stochastic system, time preferences, long-run average. 
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     author = {E. S. Palamarchuk},
     title = {Optimal linear-quadratic regulator for a~stochastic system under mutually inverse time preferences in the cost},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {38--56},
     publisher = {mathdoc},
     volume = {68},
     number = {1},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2023_68_1_a2/}
}
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E. S. Palamarchuk. Optimal linear-quadratic regulator for a~stochastic system under mutually inverse time preferences in the cost. Teoriâ veroâtnostej i ee primeneniâ, Tome 68 (2023) no. 1, pp. 38-56. http://geodesic.mathdoc.fr/item/TVP_2023_68_1_a2/