Control structure in optimization problems of bar systems

Leszek Mikulski

International Journal of Applied Mathematics and Computer Science (2004)

  • Volume: 14, Issue: 4, page 515-529
  • ISSN: 1641-876X

Abstract

top
Optimal design problems in mechanics can be mathematically formulated as optimal control tasks. The minimum principle is employed in solving such problems. This principle allows us to write down optimal design problems as Multipoint Boundary Value Problems (MPBVPs). The dimension of MPBVPs is an essential restriction that decides on numerical difficulties. Optimal control theory does not give much information about the control structure, i.e., about the sequence of the forms of the right-hand sides of state equations appearing successively in time. The correctness of the assumed control structure can be checked after obtaining the solution of the boundary problem. For the numerical solution, we use hybrid procedures which are a connection of the multiple shooting method with that of collocation.

How to cite

top

Mikulski, Leszek. "Control structure in optimization problems of bar systems." International Journal of Applied Mathematics and Computer Science 14.4 (2004): 515-529. <http://eudml.org/doc/207716>.

@article{Mikulski2004,
abstract = {Optimal design problems in mechanics can be mathematically formulated as optimal control tasks. The minimum principle is employed in solving such problems. This principle allows us to write down optimal design problems as Multipoint Boundary Value Problems (MPBVPs). The dimension of MPBVPs is an essential restriction that decides on numerical difficulties. Optimal control theory does not give much information about the control structure, i.e., about the sequence of the forms of the right-hand sides of state equations appearing successively in time. The correctness of the assumed control structure can be checked after obtaining the solution of the boundary problem. For the numerical solution, we use hybrid procedures which are a connection of the multiple shooting method with that of collocation.},
author = {Mikulski, Leszek},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {optimization; elastic structures; minimum principle},
language = {eng},
number = {4},
pages = {515-529},
title = {Control structure in optimization problems of bar systems},
url = {http://eudml.org/doc/207716},
volume = {14},
year = {2004},
}

TY - JOUR
AU - Mikulski, Leszek
TI - Control structure in optimization problems of bar systems
JO - International Journal of Applied Mathematics and Computer Science
PY - 2004
VL - 14
IS - 4
SP - 515
EP - 529
AB - Optimal design problems in mechanics can be mathematically formulated as optimal control tasks. The minimum principle is employed in solving such problems. This principle allows us to write down optimal design problems as Multipoint Boundary Value Problems (MPBVPs). The dimension of MPBVPs is an essential restriction that decides on numerical difficulties. Optimal control theory does not give much information about the control structure, i.e., about the sequence of the forms of the right-hand sides of state equations appearing successively in time. The correctness of the assumed control structure can be checked after obtaining the solution of the boundary problem. For the numerical solution, we use hybrid procedures which are a connection of the multiple shooting method with that of collocation.
LA - eng
KW - optimization; elastic structures; minimum principle
UR - http://eudml.org/doc/207716
ER -

References

top
  1. Bulirsch R. and Montrone F. and Pesch H.J. (1991): Abort landing in the presence of a wind shearas a minimax optimal control problem. Part 1: Necessary conditions. -Optim. Theory Applic., Vol. 70, No. 1, pp. 1-23. Zbl0726.49014
  2. Buss M., Glocker M., Hardt M., Von Stryk O., Bulirsch R., Schmidt G. (2002): Nonlinear hybrid dynamical systems: Modeling, optimal control, and applications, In: Modelling, Analysis and Design of Hybrid Systems: (S. Engell, G. Frehse, E. Schnieder, Eds.). - Berlin: Springer, pp. 311-335. 
  3. Hiltman P., Chudej K., Breitner M. (1993): Eine modifizierte Mehrzielmethode zur Losung von Mehrpunkt - Randwertproblemen - Benuzeranleitung. - Sonderforschungsbereich 255 DFG, TU Munchen, Report 14. 
  4. Hinsberger H. (1996): Ein direktes Mehrschiessverfahren zur Losung von Optimalsteuerungsproblemen - DIRMUS - Benutzeranleitung. - TU Clausthal. 
  5. Malanowski K., Maurer, H. (1998): Sensitivity analysis for optimal control problems subject to higher order state constraints.- Echtzeit-Optimierung grosser Systeme, DFG, Preprint 98-5, 1-32, available at: http://www.zib.de/dfg-echtzeit 
  6. Mikulski L. (1999): Optimal design of elastic continuous structures.- TU Cracow, Series Civil Engineering, Monograph 259. 
  7. Oberle H.J., Grimm, W. (1989): BNDSCO - A program for the numerical solution of optimal control problems. - Deutsche Forschungsanstalt fur Luft und Raumfahrt, DLR IB 515-8922, Oberpfaffenhofen. 
  8. Pesch H.J. (1994): A practical guide to the solution of real-life optimal control problems. - Contr. Cybern., Vol. 23, Nos. 1-2, pp. 7-60. Zbl0811.49029
  9. Pesch H.J. (2002): Schlussel Technologie Mathematik. -Stuttgart-Leipzig-Wiesbaden: Teubner Verlag. 
  10. Von Stryk O. (2002): User's guide DIRCOL - A direct collocation method for the numerical solution of optimal control problems. - Technische Universitat Darmstadt, Fachgebiet Simulation und System-optimierung (SIM), Ver. 2.1. 

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.