Geodesic
On optimal stochastic linear quadratic control with inversely proportional time-weighting in the cost
Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 1, pp. 37-56

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We consider an optimal linear-quadratic control problem for a control system where the matrices corresponding to the state in the controlled process equation and the cost functional are absolutely integrable over an infinite time interval. The integral quadratic performance index includes two mutually inversely proportional time-weighting functions. It is shown that a well-known linear stable feedback law turns out to be optimal with respect to criteria from the class of the extended long-run averages. The results are applied to studying a control system under time-varying dynamic scaling of its parameters.
Keywords: stochastic linear-quadratic regulator, pathwise optimality, inversely proportional time-weighting of costs, absolutely integrable state matrix. 
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     author = {E. S. Palamarchuk},
     title = {On optimal stochastic linear quadratic control with inversely proportional time-weighting in the cost},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {37--56},
     publisher = {mathdoc},
     volume = {67},
     number = {1},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_2022_67_1_a2/}
}
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E. S. Palamarchuk. On optimal stochastic linear quadratic control with inversely proportional time-weighting in the cost. Teoriâ veroâtnostej i ee primeneniâ, Tome 67 (2022) no. 1, pp. 37-56. http://geodesic.mathdoc.fr/item/TVP_2022_67_1_a2/