Computation and approximation of piecewise affine control laws via binary search trees

Proceedings of the IEEE Conference on Decision and Control

Volumn 3, Issue , 2002, Pages 3144-3149

  Tondel P ^a   Johansen, T A ^a   Bemporad, A ^b  

^a NORWEGIAN UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Norway)

^b UNIVERSITY OF SIENA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHMS; APPROXIMATION THEORY; COMPUTATIONAL METHODS; DATA STRUCTURES; OPTIMIZATION; PIECEWISE LINEAR TECHNIQUES; POLYNOMIALS; THEOREM PROVING; TREES (MATHEMATICS);

BINARY SEARCH TREE; MODEL PREDICTIVE CONTROL; PIECEWISE AFFINE CONTROL LAW; PIECEWISE NONLINEAR FUNCTION;

CONTROL THEORY;

EID: 0242417082     PISSN: 01912216     EISSN: None     Source Type: Conference Proceeding    
DOI: None     Document Type: Conference Paper

References (22)

1. A. Bemporad, M. Morari, V. Dua, and E. Pistikopoulos, "The explicit linear quadratic regulator for constrained systems," Automatica, vol. 38, no. 1, pp. 3-20, 2002.
2. P. Tøndel, T. A. Johansen, and A. Bemporad, "An algorithm for multi-parametric quadratic programming and explicit MPC solutions," in Proc. 40th IEEE Conf. on Decision and Control, (Orlando, Fl), 2001.
3. T. A. Johansen, I. Petersen, and O. Slupphaug, "Explicit suboptimal linear quadratic regulation with input and state constraints," Automatica, vol. 38, no. 7, pp. 1099-1111, 2002.
4. M. M. Seron, J. D. Doná, and G. Goodwin, "Global analytical model predictive control with input constraints," in Proc. 39th IEEE Conf. on Decision and Control, (Sydney), 2000.
5. A. Bemporad and C. Filippi, "Suboptimal explicit RHC via approximate multiparametric quadratic programming," Journal of Optimization Theory and Applications, In press.
6. T. A. Johansen and A. Grancharova, "Approximate explicit model predictive control implemented via orthogonal search tree partitioning," in Preprints XV IFAC World Congress, (Barcelona), 2002.
7. A. Bemporad, F. Borrelli, and M. Morari, "Model predictive control based on linear programming - the explicit solution," IEEE Trans. Automatic Control, In press.
8. A. Bemporad, F. Borrelli, and M. Morari, "Optimal controllers for hybrid systems: Stability and piecewise linear explicit form," in Proc. 39th IEEE Conf. on Decision and Control, 2000.
9. A. Bemporad, F. Borelli, and M. Morari, "Piecewise linear robust model predictive control," in Proc. European Control Conference, (Porto, Portugal), Oct. 2001.
10. G. Garcia and S. Tarbouriech, "Piecewise-linear robust control of systems with input constraints," European Journal of Control, vol. 5, no. 1, pp. 157-166, 1999.
11. G. Wredenhagen and P. Belanger, "Piecewise-linear LQ control for systems with input constraints," Automatica, vol. 30, no. 3, pp. 403-416, 1994.
12. A. Rantzer and M. Johansson, "Piecewise linear quadratic optimal control," IEEE Trans. Automatic Control, vol. 45, pp. 629-637, 2000.
13. A. Hassibi and S. Boyd, "Quadratic stabilization and control of piecewise linear systems," in Proceedings American Control Conference, 1998.
14. O. Slupphaug and B. A. Foss, "Quadratic stabilization of discrete-time uncertain nonlinear multi-model systems using piecewise affine state feedback," Int. J. Control, vol. 72, pp. 686-701, 1999.
15. F. Borrelli, M. Baotic, A. Bemporad, and M. Morari, "Efficient on-line computation of explicit model predictive control," in Proc. 40th IEEE Conf. on Decision and Control, (Orlando, Florida), 2001.
16. J. Snoeyink, "Point location," in Handbook of Discrete and Computational Geometry (J. E. Goodman and J. O'Rourke, eds.), ch. 30, pp. 559-574, CRC Press LLC, 1997.
17. M. T. Goodrich and K. Ramaiyer, "Point location," in Handbook of Computational Geometry (J.-R. Sack and J. Urrutia, eds.), pp. 121 - 153, Amsterdam: Elsevier Science Publishers B. V. North-Holland, 1999.
18. P. Tøndel and T. A. Johansen, "Complexity reduction in explicit linear model predictive control," in Preprints XV IFAC World Congress, (Barcelona), 2002.
19. A. Vicino and G. Zappa, "Sequential approximation of feasible parameter sets for identification with set membership uncertainty," IEEE Trans. Automatic Control, vol. 41 pp. 774-785, 1996.
20. A. V. Aho, J. E. Hopcroft, and J. D. Ullman, Data Structures and Algorithms, Reading, MA.: Addison-Wesley, 1983.
21. A. Bemporad, K. Fukuda, and F.D. Torrisi, "Convexity recognition of the union of polyhedra," Computational Geometry, no. 18, pp. 141-154, 2001.
22. F. Borrelli, A. Bemporad, M. Fodor, and D. Hrovat, "A hybrid approach to traction control," in Proc. 4th International Workshop on Hybrid Systems: Comp. and Control, (Rome), 2001.