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Original Articles

Robust optimal control for minimax stochastic linear quadratic problem

Pages 1054-1065 | Published online: 08 Nov 2010

References

  • BA?AR , T. Minimax control of switching systems under sampling . Proceedings of the 33rd Conference on Decision and Control . December , Lake Buena Vista, Florida , USA. pp. 716 – 721 .
  • BELLMAN , R. 1957 . Dynamic Programming , Princeton , NJ : Princeton University Press .
  • BENSOUSSAN , A. 1933 . Lecture on Stochastic Control, Part 1 . Lectures Notes in Mathematics , 972 : 1 – 39 .
  • BERNHARD , P. Minimax versus stochastic partial information control . Proceedings of the 33rd Conference on Decision and Controls . December , Lake Buena Vista, Florida , USA. pp. 2572 – 2577 .
  • BISMUT , J. M. 1977 . Qn optimal control of linear stochastic equations with a linear quadratic criteria . SIAM Journal of Control , 15 : 1 – 4 .
  • BISMUT , J. M. 1978 . An introductory approach to duality in stochastic control . SIAM Review , 20 : 62 – 78 .
  • BLOM , H. and EVERDIJ , M. Embedding adaptive JLQG into LQ martingale with a complete observable stochastic control matrix . Proceedings of the 32nd Conference on Decision and Control . December , San Antonio, TX , USA. pp. 849 – 854 .
  • BOLTYANSKY , V. G. 1937 . The Tent method in topological vector spaces . Soviet Mathematical Doklady , 34 : 176 – 179 .
  • BOLTYANSKY , V. G. and POZNYAK , A. S. 1999a . Robust maximum principle in minimax control . International Journal of Control , 72 : 305 – 314 .
  • BOLTYANSKY , V. G. and POZNYAK , A. S. Robust maximum principle for minimax Bolza problem with terminal set . Proceedings of IF AC-99 . Beijing , China. pp. 263 – 268 . F (2d-06)
  • BOUKAS , E. K. , SHI , P. and ANDIJANI , A. 1999 . Robust inventory-production control problem with stochastic demand . Optimal Control Applications and Methods , 20 : 120
  • DIDINSKY , G. and BA?AR , T. Minimax controller and filter designs for discrete-time linear systems under soft-constrained quadratic performance indices . Proceedings of the 30th Conference on Decision and Control . Brighton , England. pp. 585 – 590 .
  • DUNCAN , T. E. , Guo , L. and PASIK-DUNCAN , B.S. 1999 . Adaptive continuous-time linear quadratic Gaussian control . IEEE Transactions on Automatic Control , 44 : 1653 – 1662 .
  • DUNCAN , T. E. and VARAIYA , P. P. 1971 . On the solution ofa stochastic control system . SIAM Journal of Control , 9 : 354 – 371 .
  • ELLIOT , R. J. and KOHLMAN , M. 1994 . The second order minimum principle and adjoint process . Stochastics and Stochastic Reports , 46 : 25 – 39 .
  • FLEMING , W. H. and RISHEL , R. W. 1975 . Optimal Deterministic and Stochastic Control. , Berlin : SpringerVerlag .
  • HAUSSMAN , U. G. 1981 . Some examples of optimal control, or: the stochastic maximum principle at work . SIAM Review , 23 : 292 – 307 .
  • KUSHNER , H. 1972 . Necessary conditions for continuous parameter stochastic optimization problems . SIAM Journal of Control , 10 : 550 – 565 .
  • PONTRYAGIN , L. S. , BOLTYANSKY , V. G. , GAMKRELIDZE , R. V. and MISHENKO , E. F. 1952 . The Mathematical Theory of Optimal Processes , New York : Interscience) (translated from Russian 1969 .
  • POZNYAK , A. S. , DUNCAN , T. E. , PASIK-DUNCAN , B. and BOLTYANSKY , V. G. 2002 . Robust stochastic maximum principle . International Journal of Control , (to be published)
  • POZNYAK , A. and TAKSAR , M. 1986 . Robust control of linear stochastic systems with fully observable state . Applications Mathematicae , 24 : 35 – 46 .
  • TAKSAR , M. L , POZNYAK , A. S. and IPARRAGUIRRE , A. 1998 . Robust output feedback control for linear stochastic systems in continuous time with time-varying parameters . IEEE Transactions on Automatic Control , 43 : 1133 – 1136 .
  • UGRINOVSII , V. A. and PETERSEN , I. R. Finite horizon minimax optimal control of nonlinear continuous time systems with stochastic uncertainties . Proceedings of 36th IEEE CDC . San Diego , USA. pp. 2265 – 2270 .
  • UGRINOVSII , V. A. and PETERSEN , I. R . 1999 . Absolute stabilization and minimax optimal control of uncertain systems with stochastic uncertainty . SIAM Journal on Control and Optimization , 37 : 1089 – 1122 .
  • WILLEMS , J. C. 1971 . Least squares optimal control and algebraic Riccati equations . IEEE Transactions on Automatic Control , 16 : 621 – 634 .
  • YAZ , G. Minimax control of discrete nonlinear stochastic systems with white noise uncertainty . Proceedings of the 30th Conference on Decision and Control . Brighton , England. pp. 1815 – 1816 .
  • YONG , J. and ZHOU , X. Y. 1999 . stochastic Controls: Hamiltonian Systems and HJB Equations , Springer-Verlag .
  • ZHOU , X. Y. 1991 . A. unified treatment of maximum principle and dynamic programming in stochastic controls . Stochastics and Stochastic Reports , 36 : 137 – 161 .

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