<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>A class of finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with a single point delay in the state variables is considered. Using a theorem and methods adopted directly from deterministic controllability problems, necessary and sufficient conditions for various kinds of stochastic relative controllability are formulated and proved. It will be demonstrated that under suitable assumptions the relative controllability of an associated deterministic linear dynamic system is equivalent to the stochastic relative exact controllability and the stochastic relative approximate controllability of the original linear stochastic dynamic system. Some remarks and comments on the existing results for the controllability of linear dynamic systems with delays are also presented. Finally, a minimum energy control problem for a stochastic dynamic system is formulated and solved.</p></abstract>

A class of finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with a single point delay in the state variables is considered. Using a theorem and methods adopted directly from deterministic controllability problems, necessary and sufficient conditions for various kinds of stochastic relative controllability are formulated and proved. It will be demonstrated that under suitable assumptions the relative controllability of an associated deterministic linear dynamic system is equivalent to the stochastic relative exact controllability and the stochastic relative approximate controllability of the original linear stochastic dynamic system. Some remarks and comments on the existing results for the controllability of linear dynamic systems with delays are also presented. Finally, a minimum energy control problem for a stochastic dynamic system is formulated and solved.

Stochastic Controllability of Linear Systems With State Delays

Institute of Control Engineering, Silesian University of Technology, ul. Akademicka 16, 44-100 Gliwice, Poland, jerzy.klamka@polsl.pl

International Journal of Applied Mathematics and Computer Science

{"article-title":"Stochastic Controllability of Linear Systems With State Delays"}

A class of finite-dimensional stationary dynamic control systems described by linear stochastic ordinary differential state equations with a single point delay...

Stochastic Controllability of Linear Systems With State Delays

Published Online: Apr 05, 2007

Page range: 5 - 13

DOI: https://doi.org/10.2478/v10006-007-0001-8

Keywords
controllability, linear control systems, stochastic control systems, delayed state variables, minimum energy control

This content is open access.

Stochastic Controllability of Linear Systems With State Delays

Published Online: Apr 05, 2007

Page range: 5 - 13

DOI: https://doi.org/10.2478/v10006-007-0001-8

Keywordscontrollability, linear control systems, stochastic control systems, delayed state variables, minimum energy control

This content is open access.

Keywords
controllability, linear control systems, stochastic control systems, delayed state variables, minimum energy control