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.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1082,
author = {Maciej Szymkat and Adam Korytowski},
title = {Evolution of structure for direct control optimization},
journal = {Discussiones Mathematicae, Differential Inclusions, Control and Optimization},
volume = {27},
year = {2007},
pages = {165-193},
zbl = {1191.49031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1082}
}
Maciej Szymkat; Adam Korytowski. Evolution of structure for direct control optimization. Discussiones Mathematicae, Differential Inclusions, Control and Optimization, Tome 27 (2007) pp. 165-193. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1082/
[000] [1] J.T. Betts, Survey of numerical methods for trajectory optimization, Journal of Guidance, Control and Dynamics 21 (2) (1998), 193-207. | Zbl 1158.49303
[001] [2] J.T. Betts, Practical Methods for Optimal Control Using Nonlinear Programming, SIAM (2001). | Zbl 0995.49017
[002] [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.
[003] [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. | Zbl 0752.49017
[004] [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.
[005] [6] C.R. Hargraves and S.W. Paris, Direct trajectory optimization using nonlinear programming and collocation, Journal of Guidance 10 (4) (1987), 338-342. | Zbl 0634.65052
[006] [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. | Zbl 1029.49029
[007] [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. | Zbl 1070.65555
[008] [9] D. Kraft, On converting optimal control problems into nonlinear programming problems, Computational Mathematics and Programming, 15 (1985), 261-280. | Zbl 0572.49015
[009] [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. | Zbl 0866.65042
[010] [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.
[011] [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.
[012] [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.
[013] [14] H. Seywald, Long flight-time range-optimal aircraft trajectories, Journal of Guidance, Control, and Dynamics 19 (1) (1996), 242-244. | Zbl 0876.70019
[014] [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.
[015] [16] H.R. Sirisena, A gradient method for computing optimal bang-bang control, International Journal of Control 19 (1974), 257-264. | Zbl 0273.49052
[016] [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.
[017] [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.
[018] [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.
[019] [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.
[020] [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.
[021] [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.
[022] [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. | Zbl 0639.49023