Control of a linear stochastic system by a probability functional
type: Item
instance of: scholarly article
title: Control of a linear stochastic system by a probability functional
zbMATH Open document ID: 0942.93046
author: A. I. Kibzun
author: A. N. Sotskij
published in: Automation and Remote Control
publication date: 2000-08-21T00:00:00Z
review text: The authors study the problem of maximization of the probability that the terminal state of a discrete-time linear stochastic system reaches a given terminal set, namely, a parallelepiped the faces of which are parallel to the coordinate axes. At each instant a suboptimal control is searched by solving a linear programming problem with parameters depending on current values of the state vector of the system. The dynamics of a linear stochastic system is described by the equation \[ x_{n+1}= A_n x_n+ B_nu_n+ \zeta_n,\quad 0\leq n\leq N<\infty, \] where \(x_n\) is the state vector of the system, \(u_n\) is a control vector, \(\zeta_n\) are normally distributed. Actually, the authors maximize the lower bound of a ``terminal'' probability, so the solution to the problem is suboptimal. Benders' decomposition is used for searching a suboptimal positional control. Numerical experiments demonstrate good effectiveness of the proposed algorithm with the probability criterion; it is better in comparison with the mean-square criterion.
Mathematics Subject Classification ID: 93E20
Mathematics Subject Classification ID: 93B03
Mathematics Subject Classification ID: 90C05
zbMATH DE Number: 1279855
zbMATH Keywords: probability reachability
zbMATH Keywords: stochastic optimal control
zbMATH Keywords: suboptimal control
zbMATH Keywords: discrete-time linear stochastic system
zbMATH Keywords: linear programming
zbMATH Keywords: Benders' decomposition
zbMATH Keywords: algorithm
reviewed by: Yuliya S. Mishura
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1279855