This article is cited in 1 paper

Stochastic Systems

Optimal controller for a nonautonomous linear stochastic system with a two-sided cost functional

E. S. Palamarchuk

Central Economics and Mathematics Institute, Moscow, Russia

Abstract: The stochastic linear control problem over an infinite-time horizon with a two-sided cost functional and a time-varying diffusion matrix is considered. In the two-sided quadratic cost functional, the limits of integration have opposite sign and depend on the length of planning horizon. It is shown that under conditions on the diffusion matrix growth, the well-known linear feedback law is optimal in terms of the extended long-run average cost and its pathwise analog. In addition, the probabilistic behavior of the system's optimal path is studied.

Keywords: stochastic linear controller, two-sided cost functional, time-varying diffusion matrix.

Presented by the member of Editorial Board: B. M. Miller

Received: 31.05.2019
Revised: 15.07.2019
Accepted: 18.07.2019

DOI: 10.31857/S0005231020010055

 English version: Automation and Remote Control, 2020, 81:1, 53–63

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