메뉴 건너뛰기




Volumn 59, Issue 1, 2010, Pages 50-56

An iterative algorithm to solve state-perturbed stochastic algebraic Riccati equations in LQ zero-sum games

Author keywords

Iterative; SARE; Stochastic

Indexed keywords

ALGEBRAIC RICCATI EQUATIONS; EXISTING METHOD; GLOBALLY CONVERGENT; INDEFINITE QUADRATIC TERM; ITERATIVE ALGORITHM; NEGATIVE SEMI-DEFINITE; NUMERICAL EXAMPLE; ZERO-SUM GAME;

EID: 74449083177     PISSN: 01676911     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.sysconle.2009.11.006     Document Type: Article
Times cited : (30)

References (29)
  • 1
    • 33747072818 scopus 로고    scopus 로고
    • Two-person zero-sum linear quadratic stochastic differential games by a Hibert space method
    • Mou L., and Yong J. Two-person zero-sum linear quadratic stochastic differential games by a Hibert space method. J. Ind. Management Optim. 2 1 (2006)
    • (2006) J. Ind. Management Optim. , vol.2 , Issue.1
    • Mou, L.1    Yong, J.2
  • 2
    • 84927725688 scopus 로고    scopus 로고
    • An iterative algorithm to solve Algebraic Riccati equations with an indefinite quadratic term
    • Greece, July
    • A. Lanzon, Y. Feng, B.D.O. Anderson, An iterative algorithm to solve Algebraic Riccati equations with an indefinite quadratic term, in: Proceedings of European Control Conference 2007, Kos, Greece, July, 2007, pp. 3033-3039
    • (2007) Proceedings of European Control Conference 2007, Kos , pp. 3033-3039
    • Lanzon, A.1    Feng, Y.2    Anderson, B.D.O.3
  • 3
    • 56549098855 scopus 로고    scopus 로고
    • Computing the positive stabilizing solution to algebraic riccati equations with an indefinite quadratic term via a recursive method
    • Lanzon A., Feng Y., Anderson B.D.O., and Rotkowitz M. Computing the positive stabilizing solution to algebraic riccati equations with an indefinite quadratic term via a recursive method. IEEE Trans. Automat. Control 53 10 (2008) 2280-2291
    • (2008) IEEE Trans. Automat. Control , vol.53 , Issue.10 , pp. 2280-2291
    • Lanzon, A.1    Feng, Y.2    Anderson, B.D.O.3    Rotkowitz, M.4
  • 6
    • 84914965022 scopus 로고
    • On an iterative technique for Riccati equation computation
    • Kleinman D.L. On an iterative technique for Riccati equation computation. IEEE Trans. Automat. Control 13 (1968) 114-115
    • (1968) IEEE Trans. Automat. Control , vol.13 , pp. 114-115
    • Kleinman, D.L.1
  • 7
    • 33747065301 scopus 로고    scopus 로고
    • Generalized Riccati equations arising in stochastic games
    • McAsey M., and Mou L. Generalized Riccati equations arising in stochastic games. J. Linear Algebra Appl. 416 2-3 (2006) 710-723
    • (2006) J. Linear Algebra Appl. , vol.416 , Issue.2-3 , pp. 710-723
    • McAsey, M.1    Mou, L.2
  • 8
    • 62749156426 scopus 로고    scopus 로고
    • Stability of a random Riccati equation with markovian binary switching
    • New Orleans, LA, USA, Dec. 12-14
    • L. Xie, Lihua Xie, Stability of a random Riccati equation with markovian binary switching, in: Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, LA, USA, Dec. 12-14, 2007
    • (2007) Proceedings of the 46th IEEE Conference on Decision and Control
    • Xie, L.1    Xie, L.2
  • 9
    • 0043235563 scopus 로고    scopus 로고
    • On stability of Random Riccati equations
    • Wang Y., and Guo L. On stability of Random Riccati equations. Sci. China Ser. E 42 2 (1999)
    • (1999) Sci. China Ser. E , vol.42 , Issue.2
    • Wang, Y.1    Guo, L.2
  • 10
    • 0000679502 scopus 로고    scopus 로고
    • Global solutions to a game-theoretic Riccati equation of stochastic control
    • Dragan V., and Morozan T. Global solutions to a game-theoretic Riccati equation of stochastic control. J. Differential Equations 138 (1997) 328-350
    • (1997) J. Differential Equations , vol.138 , pp. 328-350
    • Dragan, V.1    Morozan, T.2
  • 11
    • 50249105907 scopus 로고    scopus 로고
    • Stochastic Nash games with state-dependent noise
    • Sept. 17-20, Japan
    • M. Sagara, H. Mukaidani, T. Yamamoto, Stochastic Nash games with state-dependent noise, in: SICE Annual Conference 2007, Sept. 17-20, Japan, 2007
    • (2007) SICE Annual Conference
    • Sagara, M.1    Mukaidani, H.2    Yamamoto, T.3
  • 12
    • 39449107830 scopus 로고    scopus 로고
    • Numerical solution of stochastic Nash games with state-dependent noise for weakly coupled large-scale systems
    • Sagara M., Mukaidani H., and Yamamoto T. Numerical solution of stochastic Nash games with state-dependent noise for weakly coupled large-scale systems. Appl. Math. Comput. 197 (2008) 844-857
    • (2008) Appl. Math. Comput. , vol.197 , pp. 844-857
    • Sagara, M.1    Mukaidani, H.2    Yamamoto, T.3
  • 13
    • 0001042840 scopus 로고
    • On a matrix Riccati equation of stochastic control
    • Wonham W.M. On a matrix Riccati equation of stochastic control. SIAM J. Control 6 4 (1968) 681-697
    • (1968) SIAM J. Control , vol.6 , Issue.4 , pp. 681-697
    • Wonham, W.M.1
  • 17
    • 0031673832 scopus 로고    scopus 로고
    • A new approach to linearly perturbed Riccati equations in stochastic control
    • Fragoso M.D., Costa O.L.V., and de Souza C.E. A new approach to linearly perturbed Riccati equations in stochastic control. Appl. Math. Optim. 37 (1998) 99-126
    • (1998) Appl. Math. Optim. , vol.37 , pp. 99-126
    • Fragoso, M.D.1    Costa, O.L.V.2    de Souza, C.E.3
  • 19
    • 0242440094 scopus 로고    scopus 로고
    • On stabilizability and exact obervability of stochastic systems with their applications
    • Zhang W., and Chen B.S. On stabilizability and exact obervability of stochastic systems with their applications. Automatica 40 1 (2004) 87-94
    • (2004) Automatica , vol.40 , Issue.1 , pp. 87-94
    • Zhang, W.1    Chen, B.S.2
  • 20
    • 1642290752 scopus 로고
    • Stabilization of linear systems with multiplicative noise under incomplete information
    • Ryashko L.B. Stabilization of linear systems with multiplicative noise under incomplete information. J. Appl. Math. Mech. 45 (1981) 778-786
    • (1981) J. Appl. Math. Mech. , vol.45 , pp. 778-786
    • Ryashko, L.B.1
  • 21
    • 85128534625 scopus 로고    scopus 로고
    • Y. Feng, B.D.O. Anderson, An iterative algorithm to solve periodic differential Riccati equtaions with a sign indefinite qudaratic term, in: Proceedings of Conference of Decision and Control, Cancun, Mexico, 2008, pp. 339-344
    • Y. Feng, B.D.O. Anderson, An iterative algorithm to solve periodic differential Riccati equtaions with a sign indefinite qudaratic term, in: Proceedings of Conference of Decision and Control, Cancun, Mexico, 2008, pp. 339-344
  • 24
    • 33747903611 scopus 로고    scopus 로고
    • A note on the solution of the stochastic algebraic Riccati equation
    • Zhang W., and Jia L. A note on the solution of the stochastic algebraic Riccati equation. Asian J. Control 2 4 (2000)
    • (2000) Asian J. Control , vol.2 , Issue.4
    • Zhang, W.1    Jia, L.2
  • 26
    • 0033269095 scopus 로고    scopus 로고
    • Solutions for the linear-quadratic control problems of markov jump linear systems
    • DoVal J.B.R., Geromel J.C., and Costa O.L.V. Solutions for the linear-quadratic control problems of markov jump linear systems. J. Optim. Theory Appl. 103 (1999) 283-311
    • (1999) J. Optim. Theory Appl. , vol.103 , pp. 283-311
    • DoVal, J.B.R.1    Geromel, J.C.2    Costa, O.L.V.3
  • 28
    • 0032166520 scopus 로고    scopus 로고
    • ∞-control in the presence of stochastic uncertainty
    • ∞-control in the presence of stochastic uncertainty. Internat. J. Control 71 2 (1998) 219-237
    • (1998) Internat. J. Control , vol.71 , Issue.2 , pp. 219-237
    • Ugrinovskii, V.A.1
  • 29
    • 0032690853 scopus 로고    scopus 로고
    • Absolute stabilization and minimax optimal control of uncertain systems with stochastic uncertainty
    • Ugrinovskii V.A., and Petersen I.R. Absolute stabilization and minimax optimal control of uncertain systems with stochastic uncertainty. SIAM J. Control Optim. 37 4 (1999) 1089-1122
    • (1999) SIAM J. Control Optim. , vol.37 , Issue.4 , pp. 1089-1122
    • Ugrinovskii, V.A.1    Petersen, I.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.