Optimal control of Markov jump with multiplicative noise systems with indefinite quadratic and linear costs

Author

Costa, O.L.V. ; De Paulo, W. Lima

Author_Institution

Dept. de Engenharia de Telecomunicanoes e Controle, Univ. de Sao Paulo

fYear

2006

fDate

14-16 June 2006

Abstract

In this paper we consider the stochastic optimal control problem of discrete-time Markov jump with multiplicative noise linear systems. The performance criterion is assumed to be formed by a linear combination of a quadratic part and a linear part in the state and control variables. The weighting matrices of the state and control for the quadratic part are allowed to be indefinite. We present a necessary and sufficient condition under which the problem is well-posed and a state feedback solution can be derived from a set of coupled generalized Riccati difference equations interconnected with a set of coupled linear recursive equations

Keywords

Markov processes; Riccati equations; difference equations; discrete time systems; linear quadratic control; linear systems; matrix algebra; recursive functions; state feedback; Markov process; control variables; discrete-time Markov jump; generalized Riccati difference equations; indefinite stochastic linear quadratic control; linear recursive equations; multiplicative noise linear systems; quadratic costs; state feedback; state variables; stochastic optimal control problem; weighting matrices; Control systems; Cost function; Difference equations; Linear systems; Optimal control; Portfolios; Riccati equations; Stochastic resonance; Stochastic systems; Sufficient conditions;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2006

Conference_Location

Minneapolis, MN

Print_ISBN

1-4244-0209-3

Electronic_ISBN

1-4244-0209-3

Type

conf

DOI

10.1109/ACC.2006.1655476

Filename

1655476