Explicit solution to a linear-quadratic optimal control problem with an arbitrary terminal
type: Item
instance of: scholarly article
title: Explicit solution to a linear-quadratic optimal control problem with an arbitrary terminal
zbMATH Open document ID: 1386.49036
DOI: 10.3103/S0027132217050060
author: A. Z. Asekov
published in: Moscow University Mathematics Bulletin
publication date: 2018-03-01T00:00:00Z
review text: The author presents an explicit solution to an optimal stochastic control problem in which the optimized system is described by a linear stochastic differential equation with Wiener disturbances and the performance index is a sum of a quadratic integral functional and arbitrary terminal term. The line of reasoning goes through the Hamilton-Jacobi-Bellman equation ``linearized'' by the logarithmic transformation of the cost-to-go function. This equation could be solved by a solution to a Cauchy problem for an evolutionary equation [\textit{R. Cordero-Soto} et al., Ann. Phys. 325, No. 9, 1884--1912 (2010; Zbl 1198.81084)] with a special elliptic part. The solution can be expressed through solutions of ordinary differential equations and it leads to an explicit formula for the optimal control.
Mathematics Subject Classification ID: 49K45
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 49N10
zbMATH DE Number: 6845975
zbMATH Keywords: linear-quadratic problem
zbMATH Keywords: Hamilton-Jacobi Bellman equation
zbMATH Keywords: optimal stochastic control
reviewed by: Andrzej Świerniak
MaRDI profile type: Publication
cites work: Q3880637
cites work: Quantum integrals of motion for variable quadratic Hamiltonians
cites work: Computation of Fokker-Planck equation
cites work: Explicit form of the fundamental solution to a second order parabolic operator
full work available at URL: s0027132217050060
OpenAlex ID: W2773364582
description: scientific article; zbMATH DE number 6845975