Stackelberg Game Approach to Mixed H2/H∞ Problem for Continuous-Time System (original) (raw)

References

  1. Muradore R and Picci G, Mixed H 2/H ∞ control: The discrete-time case, Systems and Control Letters, 2005, 54(1): 1–13.
    Article MathSciNet Google Scholar
  2. Doyle J C, Glover K, Francis B A, et al., Statespace solutions to standard H 2 and H ∞ control problems, IEEE Transactions on Automatic Control, 1989, 34(8): 831–847.
    Article MathSciNet Google Scholar
  3. Lu X and Zhang W H, Mixed H 2/H ∞ output-feedback control for stochastic discrete-time systems, IEEE Chinese Control and Decision Conference, San Diego CA, 2008, 4792–4796.
    Google Scholar
  4. Doyle J, Zhou K, Glover K, et al., Mixed H 2 and H ∞ performance objectives II: Optimal control, IEEE Transactions on Automatic Control, 1994, 39(8): 1575–1587.
    Article MathSciNet Google Scholar
  5. Zhou K, Glover K, Bodenheimer B, et al., Mixed H 2 and H ∞ performance objectives I: Robust performance analysis, IEEE Transactions on Automatic Control, 1994, 39(8): 1564–1574.
    Article MathSciNet Google Scholar
  6. Limebeer D J N, Anderson B D O, and Hendel B, A Nash game approach to mixed H 2/H ∞ control, IEEE Transactions on Automatic Control, 1994, 39(1): 69–82.
    Article MathSciNet Google Scholar
  7. Khargonekar P P and Rotea M A, Mixed H 2/H ∞ control: A convex optimization approach, IEEE Transactions on Automatic Control, 1991, 36(7): 824–837.
    Article MathSciNet Google Scholar
  8. Kwak N, Principal component analysis by Lp-norm maximization, IEEE Transaction on Cybernetics, 2014, 44(5): 594–609.
    Article Google Scholar
  9. Simaan M and Cruz J B, Sampled-data Nash controls in nonzero-sum differential games, International Journal of Control, 1973, 17: 1201–1209.
    Article MathSciNet Google Scholar
  10. Chen C I, Jose B, and Cruz J R, Stackelberg solution for two-person games with biased information patterns, IEEE Transactions on Automatic Control, 1972, 17(6): 792–798.
    Article Google Scholar
  11. Jose B and Cruz J R, Leader-follower strategies for multilevel systems, IEEE Transactions on Automatic Control, 1978, 23(2): 244–255.
    Article MathSciNet Google Scholar
  12. Freiling G, Jank G, and Abou-Kandil H, Discrete-time Riccati equations in open-loop Nash and Stackelberg games, Europen Journal of Control, 1999, 5(1): 56–66.
    Article Google Scholar
  13. Sheng L, Zhang W H, and Gao M, Mixed H 2/H ∞ control of time-varying stochastic discretetime systems under uniform detectability, IET Control Theory and Applications, 2014, 8(17): 1866–1874.
    Article MathSciNet Google Scholar
  14. Leitmann G, On generalized Stackelberg strategy, Journal of Optimization Theory and Applications, 1978, 26(4): 443–464.
    Article MathSciNet Google Scholar
  15. Basar T and Bernhard P, H ∞ optimal control and related minimax design problems: A dynamic game approach, IEEE Transactions on Automatic Control, 1996, 41(9): 1397–1399.
    Article Google Scholar
  16. Basar T and Olsder G J, Dynamic noncooperative game theory, SIAM, 1995.
    Google Scholar
  17. Osborne M J, An Introduction to Game Theory, Oxford University Press, USA, ISBN: 0195128958, 2003.
    Google Scholar
  18. Simaan M, Cruz J B, and Jr., On the Stackelberg strategy in nonzerosum games, Journal of Optimization Theory and Applications, 1973, 11(5): 533–555.
    Article MathSciNet Google Scholar
  19. Medanic J V, Closed-loop Stackelberg strategies in linear-quadratic problems, IEEE Transactions on Automatic Control, 1978, 23(4): 632–637.
    Article Google Scholar
  20. Bagchi A and Basar T, Stackelberg strategies in linear-quadratic stochastic differential games, Journal of Optimization Theory and Applications, 1981, 35(3): 433–464.
    Article MathSciNet Google Scholar
  21. Freiling G, Jank G, and Lee S R, Existence and uniqueness of open-loop Stackelberg equilibria in linear-quadratic differential games, Journal of Optimization Theory and Applications, 2001, 110(3): 515–544.
    Article MathSciNet Google Scholar
  22. Mukaidani H, Tanabata R, and Matsumoto C, Dynamic game approach of H 2/H ∞ control for stochastic discrete-time systems, IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences, 2014, E97-A(11): 2200–2211.
    Google Scholar
  23. Mukaidani H, H 2/H ∞ control of stochastic systems with multiple decision makers: A Stackelberg game approach, IEEE 52nd Annual Conference on Decision and Control, 2013, 1750–1755.
    Chapter Google Scholar
  24. Zhu H N, Zhang C K, Sun P H, et al., A Stackelberg game approach to mixed H 2/H ∞ robust control for singular bilinear systems, 2011 Trans. Tech. Publications, Switzerland, 2011, 204–210: 1839–1847.
    Google Scholar
  25. Mukaidani H, Stackelberg strategy for discrete-time stochastic system and its application to H 2/H ∞ control, Proceeding of the American Control Conference, Portland, Oregon, June, 2014.
    Google Scholar
  26. Jungers M, Trélat E, and Abou-Kandil H, A Stackelberg game approach to mixed H 2/H ∞ control, In Proceeding of the 17th IFAC World Congress, Secul, Korea, 2008.
    Google Scholar
  27. Tadmor G and Mirkin L, H ∞ control and estimation with preview — Part I: Matrix ARE solutions in continuous time, IEEE Transactions on Automatic Control, 2005, 50(1): 29–40.
    Article MathSciNet Google Scholar
  28. Tadmor G and Mirkin L, H ∞ control and estimation with preview — Part II: Fixed-size ARE solutions in discrete time, IEEE Transactions on Automatic Control, 2005, 50(1): 29–40.
    Article MathSciNet Google Scholar
  29. Zhang H, Li L, Xu J, et al., Linear quadratic regulation and stabilization of discrete-time systems with delay and multiplicative noise, IEEE Transactions on Automatic Control, 2015, 60(10): 2599–2613.
    Article MathSciNet Google Scholar

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