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A continuation/GMRES method for fast computation of nonlinear receding horizon control. (English) Zbl 1168.93340

The author deals with a numerical algorithm for nonlinear receding horizon control. The original continuous-time problem was first discretized over the horizon, and a two-point boundary-value problem was obtained to determine the sequence of control input for the discretzed problem. The proposed algorithm is demonstrated for a numerical example of a two-link arm whose dynamics is highly nonlinear. Numerical study shows that the proposed algorithm is faster than the conventional algorithms.

MSC:

93B40 Computational methods in systems theory (MSC2010)
93B51 Design techniques (robust design, computer-aided design, etc.)

Software:

KELLEY; L-BFGS
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Full Text: DOI

References:

[1] Alamir, M., Solutions of nonlinear optimal and robust control problems via a mixed collocation/DAE’s based algorithm, Automatica, 37, 1109-1115 (2001) · Zbl 0972.93021
[2] Al’Brekht, E. G., On the optimal stabilization of nonlinear systems, Journal of Applied Mathematics and Mechanics, 25, 5, 1254-1266 (1961) · Zbl 0108.10503
[3] Allgower, E. L.; Georg, K., Numerical continuation methods (1990), Springer: Springer Heiderberg · Zbl 0717.65030
[4] Ascher, U. M.; Mattheji, R. M.M.; Russel, R. D., Numerical solution of boundary value problems for ordinary differential equations (1995), SIAM: SIAM Philadelphia, PA
[5] Barrett, R.; Berry, M.; Chan, T. F.; Demmel, J.; Donato, J.; Dongarra, J.; Eijkhout, V.; Pozo, R.; Romine, C.; Van der Vorst, H., Templates for the solution of linear systems: Building blocks for iterative methods (1994), SIAM: SIAM Philadelphia, PA
[6] Beard, R. W.; Saridis, G. N.; Wen, J. T., Approximate solutions to the time-invariant Hamilton-Jacobi-Bellman equation, Journal of Optimization Theory and Applications, 96, 3, 589-626 (1998) · Zbl 0916.49021
[7] Biegler, L. T. (2000). Efficient solution of dynamic optimization and NMPC problems. In F. Allgöwer, & A. Zheng (Eds.), Nonlinear model predictive control; Biegler, L. T. (2000). Efficient solution of dynamic optimization and NMPC problems. In F. Allgöwer, & A. Zheng (Eds.), Nonlinear model predictive control · Zbl 0966.93048
[8] Cannon, M.; Kouvaritakis, B.; Lee, Y. I.; Brooms, A. C., Efficient non-linear model based predictive control, International Journal of Control, 74, 4, 361-372 (2001) · Zbl 1010.93044
[9] Diehl, M.; Bock, H. G.; Findeisen, R.; Schlöder, J. P.; Nagy, Z.; Allgöwer, F., Real-time optimization and nonlinear model predictive control of process governed by differential-algebraic equations, Journal of Process Control, 12, 4, 577-585 (2002)
[10] Fontes, F. A.C. C., A general framework to design stabilizing nonlinear model predictive controllers, Systems and Control Letters, 42, 127-143 (2001) · Zbl 0985.93023
[11] Goh, C. J., On the nonlinear optimal regulator problem, Automatica, 29, 3, 751-756 (1993) · Zbl 0771.93027
[12] Imae, J., & Takahashi, J. (1999). A design method for nonlinear \(H_∞\)Proceedings of the 38th IEEE conference on decision and control; Imae, J., & Takahashi, J. (1999). A design method for nonlinear \(H_∞\)Proceedings of the 38th IEEE conference on decision and control
[13] Kelley, C. T., Iterative methods for linear and nonlinear equations, Frontiers in applied mathematics, Vol. 16 (1995), SIAM: SIAM Philadelphia, PA · Zbl 0832.65046
[14] Kreisselmeier, G.; Birkhölzer, T., Numerical nonlinear regulator design, IEEE Transactions on Automatic Control, 39, 1, 33-46 (1994) · Zbl 0796.93034
[15] Liu, D. C.; Nocedal, J., On the limited memory method for large scale optimization, Mathematical Programming B, 45, 3, 503-528 (1989) · Zbl 0696.90048
[16] Lu, P., Optimal predictive control of continuous nonlinear systems, International Journal of Control, 62, 3, 633-649 (1995) · Zbl 0830.93028
[17] Mayne, D. Q.; Rawlings, J. B.; Rao, C. V.; Scokaert, P. O.M., Constrained model predictive controlStability and optimality, Automatica, 36, 6, 789-814 (2000) · Zbl 0949.93003
[18] Meadows, E. S., & Rawlings, J. B. (1997). Model predictive control. In M. A. Henson, & D. E. Seborg (Eds.), Nonlinear process control; Meadows, E. S., & Rawlings, J. B. (1997). Model predictive control. In M. A. Henson, & D. E. Seborg (Eds.), Nonlinear process control · Zbl 0876.93064
[19] Miele, A.; Mangiavacchi, A.; Aggarwal, A. K., Modified quasi-linearization algorithm for optimal control problems with nondifferential constraints, Journal of Optimization Theory and Applications, 14, 5, 529-556 (1974) · Zbl 0281.49016
[20] Nash, S. G. (1984a). http://www.netlib.org/opt/tn; Nash, S. G. (1984a). http://www.netlib.org/opt/tn
[21] Nash, S. G., Newton-type minimization via the Lanczos algorithm, SIAM Journal of Numerical Analysis, 21, 4, 770-788 (1984) · Zbl 0558.65041
[22] Nocedal, J. (1990). http://www.netlib.org/opt/lbfgs_um.shar; Nocedal, J. (1990). http://www.netlib.org/opt/lbfgs_um.shar
[23] Ohtsuka, T., Time-variant receding-horizon control of nonlinear systems, Journal of Guidance, Control, and Dynamics, 21, 1, 174-176 (1998) · Zbl 0919.49013
[24] Ohtsuka, T. (2000). http://www-newton.mech.eng.osaka-u.ac.jp/ ohtsuka/code/index.htm; Ohtsuka, T. (2000). http://www-newton.mech.eng.osaka-u.ac.jp/ ohtsuka/code/index.htm
[25] Ohtsuka, T.; Fujii, H. A., Stabilized continuation method for solving optimal control problems, Journal of Guidance, Control, and Dynamics, 17, 5, 950-957 (1994) · Zbl 0822.49025
[26] Ohtsuka, T.; Fujii, H. A., Real-time optimization algorithm for nonlinear receding-horizon control, Automatica, 33, 6, 1147-1154 (1997) · Zbl 0879.93017
[27] Qin, S. J., & Badgwell, T. A. (2000). An overview of nonlinear model predictive control applications. In F. Allgöwer, & A. Zheng (Eds.), Nonlinear model predictive control; Qin, S. J., & Badgwell, T. A. (2000). An overview of nonlinear model predictive control applications. In F. Allgöwer, & A. Zheng (Eds.), Nonlinear model predictive control
[28] Richter, S. L.; DeCarlo, R. A., Continuation methodsTheory and applications, IEEE Transactions on Automatic Control, AC-28, 6, 660-665 (1983)
[29] Tousain, R. L., & Bosgra, O. H. (2000). Efficient dynamic optimization for nonlinear model predictive control—application to a high-density poly-ethylene grade change problem. In Proceedings of the 39th IEEE conference on decision and control; Tousain, R. L., & Bosgra, O. H. (2000). Efficient dynamic optimization for nonlinear model predictive control—application to a high-density poly-ethylene grade change problem. In Proceedings of the 39th IEEE conference on decision and control
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