On multi-parametric nonlinear programming and explicit nonlinear model predictive control

Proceedings of the IEEE Conference on Decision and Control

Volumn 3, Issue , 2002, Pages 2768-2773

  Johansen, Tor A ^a  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; BOUNDARY CONDITIONS; CONSTRAINT THEORY; NONLINEAR PROGRAMMING; ORDINARY DIFFERENTIAL EQUATIONS; PIECEWISE LINEAR TECHNIQUES; PREDICTIVE CONTROL SYSTEMS; STATE FEEDBACK; STATE SPACE METHODS; VECTORS;

MODEL PREDICTIVE CONTROL; MULTIPARAMETRIC NONLINEAR PROGRAMMING; NONLINEAR OPTIMIZATION; QUADRATIC APPROXIMATION;

NONLINEAR CONTROL SYSTEMS;

EID: 0036996308     PISSN: 01912216     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (24)

1. T. Gal, Postoptimal analyses, parametric programming and related topics, Berlin: de Gruyter, 1995.
2. A. Bemporad, M. Morari, V. Dua, and E. N. Pistikopoulos, "The explicit solution of model predictive control via multiparametric quadratic programming," in Proc. American Control Conference, Chicago, 2000, pp. 872-876.
3. P. Tøndel, T. A. Johansen, and A. Bemporad, "An algorithm for multi-parametric quadratic programming and explicit MPC solutions," in Proc. IEEE Conf. Decision and Control, Orlando, 2001, pp. TuP11-4.
4. A. Bemporad, M. Morari, V. Dua, and E. N. Pistikopoulos, "The explicit linear quadratic regulator for constrained systems," Automatica, vol. 38, pp.3-20, 2002.
5. A. Bemporad, F. Borrelli, and M. Morari, "Optimal controllers for hybrid systems: Stability and piecewise linear explicit form," in Proc. Conference on Decision and Control, Sydney, 2000.
6. A. Kojima and M. Morari, "LQ control for constrained continuous-time systems: An approach based on singular value decomposition," in Proc. IEEE Conf. Decision and Control, Orlando, 2001, pp. FrP08-3.
7. A. V. Fiacco, Introduction to sensitivity and stability analysis in nonlinear programming, Orlando, Fl: Academic Press, 1983.
8. E. S. Levitin, Perturbation theory in mathematical programming, Wiley, 1994.
9. J. Guddat, F. Guerra Vazquez, and H. Th. Jongen, Parametric optimization: Singularities, pathfollowing and jumps, Wiley, 1990.
10. A. Bemporad and C. Filippi, "Suboptimal explicit MPC via approximate quadratic programming," in Proc. IEEE Conf. Decision and Control, Orlando, 2001, pp. FrP08-5.
11. T. A. Johansen and A. Grancharova, "Approximate explicit model predictive control implemented via orthogonal search tree partitioning," in Preprints, IFAC World Congress, Barcelona, 2002, http://www.itk.ntnu.no/ansatte/Johansen_Tor.Arne/mpqp-tree-ifac.pdf.
12. T.A. Johansen, I. Petersen, and O. Slupphaug, "On explicit suboptimal LQR with state and input constraints," in Proc. IEEE Conf. Decision and Control, Sydney, 2000, pp. TuM05-6.
13. T. Parisini and R. Zoppoli, "A receding-horizon regulator for nonlinear systems and a neural approximation," Automatica, vol. 31, pp. 1443-1451, 1995.
14. T. Parisini and R. Zoppoli, "Neural approximations for multistage optimal control of nonlinear stochastic systems," IEEE Trans. on Automatic Control, vol. 41, pp. 889-895, 1996.
15. D. P. Bertsekas and J. N. Tsitsiklis, Neuro-dynamic Programming, Athena Scientific, Belmont, 1998.
16. D. Kraft, "On converting optimal control problems into nonlinear programming problems," in Computational Mathematical Programming, K. Schittkowski, Ed., vol. F15, pp. 261-280. NATO ASI Series, Springer-Verlag, 1985.
17. J. Nocedal and S. J. Wright, Numerical Optimization, Springer-Verlag, New York, 1999.
18. M. Kojima, "Strongly stable stationary solutions in nonlinear programs," in Analysis and Computation of Fixed Points, S. M. Robinson, Ed., pp. 93-138. Academic Press, New York, 1980.
19. D. Ralph and S. Dempe, "Directional derivatives of the solution of a parametric nonlinear program," Mathematical Programming, vol. 70, pp. 159-172, 1995.
20. O. L. Mangasarian and J. B. Rosen, "Inequalities for stochastic nonlinear programming problems," Operations Research, vol. 12, pp. 143-154, 1964.
21. R. T. Rockafellar, Convex Analysis, Princeton University Press, New Jersey, 1970.
22. E. M. Greitzer, "Surge and rotating stall in axial flow compressors, part i: Theoretical compression system model," J. Engineering for Power, vol. 98, pp. 190-198, 1976.
23. J. T. Gravdahl and O. Egeland, "Compressor surge control using a close-coupled valve and backstepping," in Proc. American Control Conference, Albuquerque, NM., 1997, vol. 2, pp. 982-986.
24. P. Tøndel, T. A. Johansen, and A. Bemporad, "Evaluation of piecewise affine control via binary search tree," Automatica, vol. 39, pp. accepted for publication, 2003.