Quadratic control with partial information for discrete-time jump systems with the Markov chain in a general Borel space

Author(s)

do Valle Costa, Oswaldo Luiz ^[1] ; Figueiredo, Danilo Zucolli ^[1]

Affiliation

^[1] Univ Sao Paulo, Escola Politecn, Dept Engn Telecomunicacoes & Controle, BR-05508010 Sao Paulo - Brazil

• Document type: Journal article
• Source: AUTOMATICA; v. 66, p. 73-84, APR 2016.
• Web of Science Citations: 5

Abstract

This paper deals with the finite horizon quadratic 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 4. It is assumed that the controller has access to an output variable as well as the jump parameter. The goal is to design a dynamic Markov jump controller such that the closed loop system minimizes the quadratic functional cost of the system over a finite horizon period of time. It is shown that an optimal controller can be obtained from two 4-coupled difference Riccati equations, one associated to a filtering problem and the other one associated to a control problem in which the state variable is fully available. By s-coupled it is meant that the difference Riccati equations are coupled via an integral over 4. This result, which can be seen as a separation principle for discrete-time MJLS, generalizes previous ones that were restricted to the Markov chain taking values in a finite set. (C) 2015 Elsevier Ltd. All rights reserved. (AU)

• 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