Multi-objective decision-making problems for discrete-time stochastic systems with state- and disturbance-dependent noise
- 1 December 2011
- conference paper
- conference paper
- Published by Institute of Electrical and Electronics Engineers (IEEE)
- p. 6388-6393
- https://doi.org/10.1109/cdc.2011.6160358
Abstract
In this paper, we consider three types of infinite-horizon multi-objective decision-making problems for a class of discrete-time linear stochastic systems with state- and disturbance-dependent noise. First, the H 2 /H ∞ control problem with multiple decision makers is considered. Second, in order to improve the transient response, the linear quadratic control under the Pareto solution is investigated. Finally, the soft-constrained stochastic Nash games are formulated in which robustness is attained against disturbance input. The decision strategies for the three types of problem are derived. It is found that the conditions for the existences of these strategies are related to the solutions of cross-coupled stochastic algebraic Riccati equations (CSAREs). We develop some new algorithms based on linear matrix inequality (LMI) to solve the CSAREs. Numerical example is provided to verify the efficiency of the proposed decision strategies.Keywords
This publication has 10 references indexed in Scilit:
- Mathematical Methods in Robust Control of Discrete-Time Linear Stochastic SystemsPublished by Springer Science and Business Media LLC ,2010
- Soft-constrained stochastic Nash games for weakly coupled large-scale systemsAutomatica, 2009
- Infinite horizon stochastic H2/H∞ control for discrete-time systems with state and disturbance dependent noiseAutomatica, 2008
- Generalized Coupled Algebraic Riccati Equations for Discrete-time Markov Jump with Multiplicative Noise SystemsEuropean Journal of Control, 2008
- Stochastic H2/H∞ control for discrete-time systems with state and disturbance dependent noiseAutomatica, 2007
- A numerical algorithm to find soft-constrained Nash equilibria in scalar LQ-gamesInternational Journal of Control, 2006
- Infinite Horizon LQ Optimal Control for Discrete-Time Stochastic SystemsPublished by Institute of Electrical and Electronics Engineers (IEEE) ,2006
- Mixed control: the discrete-time caseSystems & Control Letters, 2005
- Robust Equilibria in Indefinite Linear-Quadratic Differential GamesJournal of Optimization Theory and Applications, 2003
- Mixed H/sub 2//H/sub ∞/-control of discrete-time Markovian jump linear systemsIEEE Transactions on Automatic Control, 1998