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Original Articles

Optimal control of time-varying singular systems using the RK–Butcher algorithm

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Pages 617-627 | Received 28 Jun 2004, Published online: 20 Aug 2006

References

  • Chen , C. F. and Hsiao , C. H. 1975 . Walsh series analysis in optimal control . Int. J. Control , 21 : 881 – 897 .
  • Chen , W. L. and Shih , Y. P. 1978 . Analysis and optimum control of time varying linear systems via Walsh functions . Int. J. Control , 27 : 917 – 932 .
  • Cobb , D. 1983 . Descriptor variable systems and optimal state regulation . IEEE Trans. Autom. Control , 28 : 601 – 611 .
  • Pandolfi , L. 1981 . On the regulator problem for linear degenerate control systems . J. Optimi. Theory Appl. , 33 : 241 – 254 .
  • Palanisamy , K. R. 1981 . Analysis and optimal control of linear systems via single term Walsh series approach . Int. J. Syst. Sci. , 12 : 443 – 454 .
  • Balachandran , K. and Murugesan , K. 1990 . Optimal control of singular systems via single term Walsh series . Int. J. Comput. Math. , 43 : 153 – 159 .
  • Alexander , R. K. and Coyle , J. J. 1990 . Runge–Kutta methods for differential-algebraic systems . SIAM J. Numer. Anal. , 27 : 736 – 752 .
  • Butcher , J. C. 1987 . The Numerical Analysis of Ordinary Differential Equations: Runge–Kutta and General Linear Methods , Chichester : John Wiley .
  • Butcher , J. C. 2003 . Numerical Methods for Ordinary Differential Equations , Chichester : John Wiley .
  • Shampine , L. F. 1994 . Numerical Solution of Ordinary Differential Equations , New York : Chapman & Hall .
  • Yaakub , A. R. and Evans , D. J. 1999 . New Runge–Kutta starters of multi-step methods . Int. J. Comput. Math. , 71 : 99 – 104 .
  • Yaakub , A. R. and Evans , D. J. 1999 . A fourth order Runge–Kutta RK (4,4) method with error control . Int. J. Comput. Math. , 71 : 383 – 411 .
  • Bader , M. 1987 . A comparative study of new truncation error estimates and intrinsic accuracies of some higher order Runge–Kutta algorithms . Comput. Chem. , 11 : 121 – 124 .
  • Bader , M. 1998 . A new technique for the early detection of stiffness in coupled differential equations and application to standard Runge–Kutta algorithms . Theor. Chem. Acc. , 99 : 215 – 219 .
  • Murugesan , K. , Sekar , S. , Murugesh , V. and Park , J. Y. 2004 . Numerical solution of an industrial robot arm control problem using the RK–Butcher algorithm . Int. J. Comput. Appl. Technol. , 19 : 132 – 138 .
  • Park , J. Y. , Evans , D. J. , Murugesan , K. , Sekar , S. and Murugesh , V. 2004 . Optimal control of singular systems using the RK–Butcher algorithm . Int. J. Comput. Math. , 81 : 239 – 249 .
  • Shampine , L. F. and Gordon , M. K. 1975 . Computer Solutions of Ordinary Differential Equations , San Francisco, CA : W.H. Freeman .
  • El-Tohami , M. , Lovass-Nagy , V. and Mukundan , M. 1983 . On the design of observers for generalized state-space systems using singular value decomposition . Int. J. Control , 38 : 673 – 683 .
  • Lovass-Nagy , V. , Schilling , R. and Yan , H. C. 1986 . A note on optimal control of generalized state-space (descriptor) systems . Int. J. Control , 44 : 613 – 624 .

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