71
Views
12
CrossRef citations to date
0
Altmetric
Original Articles

Optimal control of singular systems using the rk–butcher algorithm

, , , &
Pages 239-249 | Received 29 Sep 2003, Published online: 12 May 2010

References

  • Alexander , R. K. and Coyle , J. J. (1990) . Runge–Kutta methods for differential-algebric systems . SIAM J. Numer. Anal. , 27 : 736 – 752 .
  • Evans , D. J. (1991) . A new Order Runge–Kutta method for initial value problems with error control . Intern. J. Comp. Math. , 139 : 217 – 227 .
  • Evans , D. J. and Yaakub , A. R. (1996) . A new fifth order weighted Runge–Kutta formula . Intern. J. Comp. Math. , 59 : 227 – 243 .
  • Evans , D. J. and Yaakub , A. R. (1998) . Weighted fifth order Runge–Kutta formulas for second order differential equations . Intern. J. Comp. Math. , 70 : 233 – 239 .
  • Hung , C. (2000) . Dissipativity of Runge–Kutta methods for dynamical systems with delays . IMA J. Numer. Anal. , 20 : 153 – 166 .
  • Murugesan , K. , Dhayabaran , D. Paul , Amirtharaj , E. C. Henry and Evans , D. J. (1999) . Analysis of different second order systems via Runge–Kutta method . Intern. J. Comp. Math. , 70 : 477 – 493 .
  • Murugesan , K. , Dhayabaran , D. Paul , Amirtharaj , E. C. Henry and Evans , D. J. (1999) . Analysis of different second order multivariable linear systems using single term Walsh Series technique and Runge–Kutta method . Intern. J. Comp. Math. , 72 : 367 – 374 .
  • Murugesan , K. , Dhayabaran , D. Paul , Amirtharaj , E. C. Henry and Evans , D. J. (2000) . Analysis of non-linear singular systems from fluid dynamics using extended Runge–Kutta methods . Intern. J. Comp. Math. , 76 : 239 – 266 .
  • Murugesan , K. , Dhayabaran , D. Paul , Amirtharaj , E. C. Henry and Evans , D. J. (2001) . A comparison of extended Runge–Kutta formulae based on variety of means to solve system of IVPs . Intern. J. Comp. Math. , 78 : 225 – 252 .
  • Murugesan , K. , Dhayabaran , D. Paul , Amirtharaj , E. C. Henry and Evans , D. J. (2002) . A fourth order embedded Runge–Kutta RKACeM(44) method based on arithmetic and centrodial means with error control . Intern. J. Comp. Math. , 79 : 247 – 269 .
  • Shampine L. F. Watts H. A. The art of writing a Runge–Kutta code, Part I Mathematical Software 3 Academic Press London (1977) 257 275
  • Shampine , L. F. and Watts , H. A. (1979) . The art of writing a Runge–Kutta code, Part II . Applied Mathematical Computations , 5 : 93 – 121 .
  • Yaakub , A. R. and Evans , D. J. (1999) . A fourth orders Runge–Kutta RK (4, 4) method with error control . Intern. J. Comp. Math. , 71 : 383 – 411 .
  • Yaakub , A. R. and Evans , D. J. (1999) . New Runge–Kutta starters of multi-step methods . Intern. J. Comp. Math. , 71 : 99 – 104 .
  • Butcher , J. C. (1964) . On Runge–Kutta processes of higher order . J. Aust. Math. Soc. , 4 : 179
  • Butcher J. C. The Numerical Analysis of Ordinary Differential Equations: Runge–Kutta and General Linear Methods John Wiley & Sons U.K. (1987)
  • Butcher , J. C. (1990) . On order reduction for Runge–Kutta methods applied to differential-algebraic systems and to stiff systems of ODE's . SIAM J. Numer. Anal. , 27 : 447 – 456 .
  • Shampine , L. F. (1985) . Some practical Runge–Kutta formulas . Math. Comp. , 46 : 135 – 150 .
  • Fehlberg , E. (1970) . Klassische Runge–Kutta-Formeln vierter und niedriger Ordnung mit Schrittweitenkontolle und ihre anwendung auf Warmeleitungsprobleme . Computing , 6 : 61 – 71 .
  • Forsythe G. E. Malcolm M. A. Moler C. D. Computer Methods for Mathematical Computations Prentice-Hall Englewood Cliffs NJ (1977)
  • 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 .
  • Balachandran , K. and Murugesan , K. (1990) . Optimal control of singular systems via single term walsh series . Intern. J. Comp. Math. , 43 : 153 – 159 .
  • Shampine L. F. Gordon M. K. Computer Solutions of Ordinary Differential Equations WH Freeman San Francisco CA (1975)
  • El-Tohami , M. , Lovass-Nagy , V. and Mukundan , R. (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 . Intern. J. Control , 44 : 613 – 624 .
  • Cobb , D. (1983) . Descriptor variable systems and optimal state regulation . IEEE Trans. Auto. Control , 28 : 601 – 611 .
  • Verghese , G.C. , Levy , B. C. and Kailath , T. (1981) . A generalized state space for singular systems . IEEE Trans. Auto. Control , 26 : 811 – 831 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.