Evolution of structure for direct control optimization

Maciej Szymkat; Adam Korytowski

Discussiones Mathematicae, Differential Inclusions, Control and Optimization (2007)

  • Volume: 27, Issue: 1, page 165-193
  • ISSN: 1509-9407

Abstract

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The paper presents the Monotone Structural Evolution, a direct computational method of optimal control. Its distinctive feature is that the decision space undergoes gradual evolution in the course of optimization, with changing the control parameterization and the number of decision variables. These structural changes are based on an analysis of discrepancy between the current approximation of an optimal solution and the Maximum Principle conditions. Two particular implementations, with spike and flat generations are described in detail and illustrated with computational examples.

How to cite

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Maciej Szymkat, and Adam Korytowski. "Evolution of structure for direct control optimization." Discussiones Mathematicae, Differential Inclusions, Control and Optimization 27.1 (2007): 165-193. <http://eudml.org/doc/271204>.

@article{MaciejSzymkat2007,
abstract = {The paper presents the Monotone Structural Evolution, a direct computational method of optimal control. Its distinctive feature is that the decision space undergoes gradual evolution in the course of optimization, with changing the control parameterization and the number of decision variables. These structural changes are based on an analysis of discrepancy between the current approximation of an optimal solution and the Maximum Principle conditions. Two particular implementations, with spike and flat generations are described in detail and illustrated with computational examples.},
author = {Maciej Szymkat, Adam Korytowski},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
keywords = {optimal control; direct optimization methods},
language = {eng},
number = {1},
pages = {165-193},
title = {Evolution of structure for direct control optimization},
url = {http://eudml.org/doc/271204},
volume = {27},
year = {2007},
}

TY - JOUR
AU - Maciej Szymkat
AU - Adam Korytowski
TI - Evolution of structure for direct control optimization
JO - Discussiones Mathematicae, Differential Inclusions, Control and Optimization
PY - 2007
VL - 27
IS - 1
SP - 165
EP - 193
AB - The paper presents the Monotone Structural Evolution, a direct computational method of optimal control. Its distinctive feature is that the decision space undergoes gradual evolution in the course of optimization, with changing the control parameterization and the number of decision variables. These structural changes are based on an analysis of discrepancy between the current approximation of an optimal solution and the Maximum Principle conditions. Two particular implementations, with spike and flat generations are described in detail and illustrated with computational examples.
LA - eng
KW - optimal control; direct optimization methods
UR - http://eudml.org/doc/271204
ER -

References

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  1. [1] J.T. Betts, Survey of numerical methods for trajectory optimization, Journal of Guidance, Control and Dynamics 21 (2) (1998), 193-207. Zbl1158.49303
  2. [2] J.T. Betts, Practical Methods for Optimal Control Using Nonlinear Programming, SIAM (2001). Zbl0995.49017
  3. [3] H.G. Bock and K.J. Plitt, A multiple shooting algorithm for direct solution of optimal control problems, IFAC 9th World Congress, Budapest, Hungary 1984. 
  4. [4] R. Bulirsch, F. Montrone and H.J. Pesch, Abort landing in the presence of a windshear as a minimax optimal control problem, part 2: multiple shooting and homotopy, Journal of Optimization Theory and Applications 70 (1991), 223-254. Zbl0752.49017
  5. [5] A. Cervantes and L.T. Biegler, Optimization Strategies for Dynamic Systems, Encyclopedia of Optimization 4 216-227, C. Floudas and P. Pardalos (eds.), Kluwer 2001. 
  6. [6] C.R. Hargraves and S.W. Paris, Direct trajectory optimization using nonlinear programming and collocation, Journal of Guidance 10 (4) (1987), 338-342. Zbl0634.65052
  7. [7] C.Y. Kaya and J.L. Noakes, Computational algorithm for time-optimal switching control, Journal of Optimization Theory and Applications 117 (1) (2003), 69-92. Zbl1029.49029
  8. [8] J. Kierzenka and L.F. Shampine, A BVP solver based on residual control and the Matlab PSE, ACM Transactions on Mathematical Software 27 (3) (2001), 299-316. Zbl1070.65555
  9. [9] D. Kraft, On converting optimal control problems into nonlinear programming problems, Computational Mathematics and Programming, 15 (1985), 261-280. Zbl0572.49015
  10. [10] R.R. Kumar and H. Seywald, Should controls be eliminated while solving optimal control problems via direct methods? Journal of Guidance, Control, and Dynamics 19 (2) (1996), 418-423. Zbl0866.65042
  11. [11] H. Maurer, C. Büskens, J.-H.R. Kim and C.Y. Kaya, Optimization methods for the verification of second order sufficient conditions for bang-bang controls, Optimal Control Applications and Methods 26 (2005), 129-156. 
  12. [12] J. Miller, A. Korytowski and M. Szymkat, Two-stage construction of aircraft thrust models for optimal control computations, Submitted to Optimal Control Applications and Methods. 
  13. [13] M. Pauluk, A. Korytowski, A. Turnau and M. Szymkat, Time optimal control of 3D crane, Proc. 7th IEEE MMAR 2001, Międzyzdroje, Poland, August 28-31 (2001), 927-932. 
  14. [14] H. Seywald, Long flight-time range-optimal aircraft trajectories, Journal of Guidance, Control, and Dynamics 19 (1) (1996), 242-244. Zbl0876.70019
  15. [15] H. Shen and P. Tsiotras, Time-optimal control of axi-symmetric rigid spacecraft with two controls, Journal of Guidance, Control and Dynamics 22 (1999), 682-694. 
  16. [16] H.R. Sirisena, A gradient method for computing optimal bang-bang control, International Journal of Control 19 (1974), 257-264. Zbl0273.49052
  17. [17] B. Srinivasan, S. Palanki and D. Bonvin, Dynamic optimization of batch processes, I. Characterization of the nominal solution, Computers and Chemical Engineering 27 (1) (2003), 1-26. 
  18. [18] O. von Stryk, User's guide for DIRCOL - a direct collocation method for the numerical solution of optimal control problems, Ver. 2.1, Technical University of Munich 1999. 
  19. [19] M. Szymkat, A. Korytowski and A. Turnau, Computation of time optimal controls by gradient matching, Proc. 1999 IEEE CACSD, Kohala Coast, Hawai'i, August 22-27 (1999), 363-368. 
  20. [20] M. Szymkat, A. Korytowski and A. Turnau, Variable control parameterization for time-optimal problems, Proc. 8th IFAC CACSD 2000, Salford, U.K., September 11-13, 2000, T4A. 
  21. [21] M. Szymkat, A. Korytowski and A. Turnau, Extended variable parameterization method for optimal control, Proc. IEEE CCA/CCASD 2002, Glasgow, Scotland, September 18-20, 2002. 
  22. [22] M. Szymkat and A. Korytowski, Method of monotone structural evolution for control and state constrained optimal control problems, European Control Conference ECC 2003, University of Cambridge, U.K., September 1-4, 2003. 
  23. [23] J. Wen and A.A. Desrochers, An algorithm for obtaining bang-bang control laws, Journal of Dynamic Systems, Measurement, and Control 109 (1987), 171-175. Zbl0639.49023

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