Indefinite quadratic with linear costs optimal control of Markov jump with multiplicative noise systems

Authors:
Oswaldo L. V. Costa;Wanderlei L. de Paulo
Affiliations:
Departamento de Engenharia de Telecomunicaçíes e Controle, Escola Politécnica da Universidade de São Paulo, 05508-970-São Paulo, SP, Brazil;Departamento de Engenharia de Telecomunicaçíes e Controle, Escola Politécnica da Universidade de São Paulo, 05508-970-São Paulo, SP, Brazil
Venue:
Automatica (Journal of IFAC)
Year:
2007

Citing 11
Cited 4

Linear quadratic problems with indefinite cost for discrete time systems

SIAM Journal on Matrix Analysis and Applications
H2 optimal control

H2 optimal control
Stochastic Linear Quadratic Regulators with Indefinite Control Weight Costs

SIAM Journal on Control and Optimization
Indefinite Stochastic Linear Quadratic Control and Generalized Differential Riccati Equation

SIAM Journal on Control and Optimization
Discrete-time Indefinite LQ Control with State and Control Dependent Noises

Journal of Global Optimization
Indefinite Stochastic Linear Quadratic Control with Markovian Jumps in Infinite Time Horizon

Journal of Global Optimization
Collecting commonsense experiences

Proceedings of the 2nd international conference on Knowledge capture
Markowitz's Mean-Variance Portfolio Selection with Regime Switching: A Continuous-Time Model

SIAM Journal on Control and Optimization
Predictive control of random-parameter systems with multiplicative noise. Application to investment portfolio optimization

Automation and Remote Control
Technical Communique: Discrete-Time Optimal Control with Control-Dependent Noise and Generalized Riccati Difference Equations

Automatica (Journal of IFAC)
Near-optimal controls of random-switching LQ problems with indefinite control weight costs

Automatica (Journal of IFAC)

Brief paper: Static output-feedback stabilization of discrete-time Markovian jump linear systems: A system augmentation approach

Automatica (Journal of IFAC)
Linear minimum mean square filter for discrete-time linear systems with Markov jumps and multiplicative noises

Automatica (Journal of IFAC)
Optimal mean-variance control for discrete-time linear systems with Markovian jumps and multiplicative noises

Automatica (Journal of IFAC)
Infinite horizon H2/H∞ control for discrete-time time-varying Markov jump systems with multiplicative noise

Automatica (Journal of IFAC)

Quantified Score

Hi-index	22.15

Visualization

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. For the case in which the quadratic-term matrices are non-negative, this necessary and sufficient condition can be written in a more explicit way. The results are applied to a problem of portfolio optimization.