H-2-control and the separation principle for discrete-time jump systems with the Markov chain in a general state space

Author(s)

Figueiredo, Danilo Zucolli ; do Valle Costa, Oswaldo Luiz

• Document type: Journal article
• Source: INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE; v. 48, n. 13, p. 2728-2741, 2017.
• Web of Science Citations: 2

Abstract

This paper deals with the H-2 optimal control problem of discrete-time Markov jump linear systems (MJLS) considering the case in which the Markov chain takes values in a general Borel space http://www.w3.org/1999/xlink. It is assumed that the controller has access only to an output variable and to the jump parameter. The goal, in this case, is to design a dynamic Markov jump controller such that the H-2-norm of the closed-loop system is minimised. It is shown that the H-2-norm can be written as the sum of two H-2-norms, such that one of them does not depend on the control, and the other one is obtained from the optimal filter for an infinite-horizon filtering problem. This result can be seen as a separation principle for MJLS with Markov chain in a Borel space http://www.w3.org/1999/xlink considering the infinite time horizon case. (AU)

• FAPESP's process: 14/50851-0 - INCT 2014: National Institute of Science and Technology for Cooperative Autonomous Systems Applied in Security and Environment
• Grantee: Marco Henrique Terra
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 14/50279-4 - Brasil Research Centre for Gas Innovation
• Grantee: Julio Romano Meneghini
• Support Opportunities: Research Grants - Research Centers in Engineering Program