Relationship Between Nash Equilibrium Strategies and H/H Control of Stochastic Markov Jump Systems With Multiplicative Noise
This technical note is concerned with discussing the relationship between Nash equilibrium strategies and the finite horizon H 2 /H ∞ control of time-varying stochastic systems subject to Markov jump parameters and multiplicative noise. It is revealed that the equivalence of these two problems depen...
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| Published in | IEEE transactions on automatic control Vol. 59; no. 9; pp. 2592 - 2597 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
IEEE
01.09.2014
The Institute of Electrical and Electronics Engineers, Inc. (IEEE) |
| Subjects | |
| Online Access | Get full text |
| ISSN | 0018-9286 1558-2523 |
| DOI | 10.1109/TAC.2014.2309274 |
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| Abstract | This technical note is concerned with discussing the relationship between Nash equilibrium strategies and the finite horizon H 2 /H ∞ control of time-varying stochastic systems subject to Markov jump parameters and multiplicative noise. It is revealed that the equivalence of these two problems depends on whether the disturbance enters into the diffusion term. Furthermore, necessary and sufficient conditions for the finite horizon H 2 /H ∞ control of stochastic Markov jump systems are presented via coupled matrix-valued equations. |
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| AbstractList | This technical note is concerned with discussing the relationship between Nash equilibrium strategies and the finite horizon H 2 /H ∞ control of time-varying stochastic systems subject to Markov jump parameters and multiplicative noise. It is revealed that the equivalence of these two problems depends on whether the disturbance enters into the diffusion term. Furthermore, necessary and sufficient conditions for the finite horizon H 2 /H ∞ control of stochastic Markov jump systems are presented via coupled matrix-valued equations. This technical note is concerned with discussing the relationship between Nash equilibrium strategies and the finite horizon $H_{2}/H_{\infty}$ control of time-varying stochastic systems subject to Markov jump parameters and multiplicative noise. It is revealed that the equivalence of these two problems depends on whether the disturbance enters into the diffusion term. Furthermore, necessary and sufficient conditions for the finite horizon $H_{2}/H_{\infty}$ control of stochastic Markov jump systems are presented via coupled matrix-valued equations. |
| Author | Ming Gao Li Sheng Weihai Zhang |
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| Cites_doi | 10.1109/TAC.2010.2041987 10.1137/S0363012998346372 10.1109/TSP.2005.851116 10.1109/TAC.2008.921024 10.1016/j.automatica.2008.01.028 10.1016/j.automatica.2012.05.006 10.1016/j.automatica.2011.11.009 10.1142/p473 10.1109/9.654895 10.1109/9.85062 10.1016/j.automatica.2007.07.001 10.4310/CIS.2002.v2.n3.a4 10.1109/TAC.2010.2046114 10.1109/TCST.2005.852116 10.1109/9.273340 10.1109/TAC.2003.821400 |
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| Keywords | Nash equilibrium strategies stochastic H_{2}/H_{\infty} control stochastic Markov jump systems Coupled Riccati equations |
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| References | ref13 ref12 du (ref4) 2005; 13 ref14 ref10 gao (ref5) 2005; 53 zhang (ref8) 2008; 44 ref2 ref1 ref17 ref16 hou (ref15) 2010; 55 ref7 dragan (ref11) 2006 ref9 ref3 ref6 |
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| Title | Relationship Between Nash Equilibrium Strategies and H/H Control of Stochastic Markov Jump Systems With Multiplicative Noise |
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