Geodesic
On optimal linear regulator with polynomial process of external excitations
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 4, pp. 672-687

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A linear control system over an infinite time-horizon is considered, where external excitations are defined as polynomials based on a time-varying Ornstein–Uhlenbeck process. An optimal control law with respect to long-run average type criteria is established. It is shown that the optimal control has the form of a linear feedback law, where the affine term satisfies a backward linear stochastic differential equation. The normalizing functions in the optimality criteria depend on the stability rate of the dynamic equation for the Ornstein–Uhlenbeck process.
Keywords: linear regulator, Ornstein–Uhlenbeck process, pathwise optimality.
Mots-clés : polynomial process 
@article{TVP_2022_67_4_a2,
     author = {E. S. Palamarchuk},
     title = {On optimal linear regulator with polynomial process of external excitations},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {672--687},
     publisher = {mathdoc},
     volume = {67},
     number = {4},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2022_67_4_a2/}
}
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E. S. Palamarchuk. On optimal linear regulator with polynomial process of external excitations. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 4, pp. 672-687. http://geodesic.mathdoc.fr/item/TVP_2022_67_4_a2/