Efficient evaluation of piecewise control laws defined over a large number of polyhedra

2007 European Control Conference, ECC 2007

Volumn , Issue , 2007, Pages 2360-2367

  Christophersen, Frank J ^a   Kvasnica, Michal ^a   Jones, Colin N ^a   Morari, Manfred ^a  

^a ETH ZURICH   (Switzerland)

Author keywords

Constrained systems; Discrete time systems; Explicit control; Hybrid systems; MPC; Multi parametric programming; Piecewise affine systems; Point location problem; Receding horizon control; Set membership test

Indexed keywords

CONTROL THEORY; CONTROLLERS; DIGITAL CONTROL SYSTEMS; FORESTRY; GEOMETRY; HYBRID SYSTEMS; LOCATION; STATE FEEDBACK; TREES (MATHEMATICS);

CONSTRAINED SYSTEMS; DISCRETE - TIME SYSTEMS; MULTI-PARAMETRIC PROGRAMMING; PIECEWISE AFFINE SYSTEMS; POINT LOCATION PROBLEMS; RECEDING HORIZON CONTROL; SET MEMBERSHIP;

DISCRETE TIME CONTROL SYSTEMS;

COMPUTATION; COMPUTER PROGRAMING; PROBLEM SOLVING;

EID: 84927748598     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.23919/ecc.2007.7068280     Document Type: Conference Paper

References (31)

1. M. Baotíc, F. J. Christophersen, and M. Morari, "A new Algorithm for Constrained Finite Time Optimal Control of Hybrid Systems with a Linear Performance Index," in Proc. of the European Control Conference, Cambridge, UK, Sept. 2003, available from http://control. ee. ethz. ch/index. cgi?page=publications.
2. A. Bemporad, C. Filippi, and F. D. Torrisi, "Inner and outer approximation of polytopes using boxes," Computational Geometry: Theory and Applications, vol. 27, no. 2, pp. 151-178, 2004.
3. A. Bemporad and M. Morari, "Control of systems integrating logic, dynamics, and constraints," Automatica, vol. 35, no. 3, pp. 407-427, Mar. 1999.
4. A. Bemporad, M. Morari, V. Dua, and E. N. Pistikopoulos, "The explicit linear quadratic regulator for constrained systems," Automatica, vol. 38, no. 1, pp. 3-20, Jan. 2002.
5. F. Borrelli, Constrained Optimal Control of Linear and Hybrid Systems, ser. Lecture Notes in Control and Information Sciences. Springer-Verlag, 2003, vol. 290.
6. F. Borrelli, M. Baotíc, A. Bemporad, and M. Morari, "Efficient On-Line Computation of Constrained Optimal Control," in Proc. of the Conf. on Decision & Control, Orlando, Florida, USA, Dec. 2001.
7. -, "An Efficient Algorithm for Computing the State Feedback Solution to Optimal Control of Discrete Time Hybrid Systems," in Proc. on the American Control Conference, Denver, Colorado, USA, June 2003, pp. 4717-4722.
8. T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, 2nd ed. MIT Press and McGraw-Hill, 2001.
9. M. de Berg, O. Schwarzkopf, M. van Kreveld, and M. Overmars, Computational Geometry: Algorithms and Applications, 2nd ed. Springer Verlag, 2000.
10. B. De Schutter and T. Van den Boom, "On model predictive control for max-min-plus-scaling discrete event systems," Automatica, vol. 37, no. 7, pp. 1049-1056, 2001.
11. G. Ferrari-Trecate, M. Muselli, D. Liberati, and M. Morari, "A clustering technique for the identification of piecewise affine systems," Automatica, vol. 39, no. 2, pp. 205-217, Feb. 2003.
12. T. Geyer, F. D. Torrisi, and M. Morari, "Efficient Mode Enumeration of Compositional Hybrid Models," in Proc. of the Intern. Workshop on Hybrid Systems: Computation and Control, ser. Lecture Notes in Computer Science, vol. 2623. Springer-Verlag, 2003, pp. 216-232.
13. -, "Optimal Complexity Reduction of Piecewise Affine Models Based on Hyperplane Arrangements," in Proc. on the American Control Conference, Boston, Massachusetts, USA, June 2004, pp. 1190-1195.
14. B. Grünbaum, Convex Polytopes, 2nd ed. Springer-Verlag, 2000.
15. W. P. M. H. Heemels, "Linear Complementarity Systems: A Study in Hybrid Dynamics," Ph. D. dissertation, Technische Universiteit Eindhoven, Eindhoven, The Netherlands, Nov. 1999.
16. W. P. M. H. Heemels, B. De Schutter, and A. Bemporad, "Equivalence of hybrid dynamical models," Automatica, vol. 37, no. 7, pp. 1085-1091, 2001.
17. O. Hermann, "Regelung eines ball and plate systems," Diploma thesis, ETH Zurich, Zurich, Switzerland, 1996.
18. R. A. Horn and C. R. Johnson, Matrix Analysis. Cambridge University Press, 1985.
19. M. Johansson, Piecewise Linear Control Systems: A Computational Approach, ser. Lecture Notes in Control and Information Sciences. Springer-Verlag, 2003, vol. 284.
20. C. N. Jones, P. Grieder, and S. V. Rakovíc, "A Logarithmic Solution to the Point Location Problem for Closed-Form Linear MPC," in IFAC World Congress, Prague, Czech Republic, July 2005.
21. E. C. Kerrigan and D. Q. Mayne, "Optimal control of constrained, piecewise affine systems with bounded disturbances," in Proc. of the Conf. on Decision & Control, Las Vegas, Nevada, USA, Dec. 2002, pp. 1552-1557.
22. M. Kvasnica, P. Grieder, and M. Baotíc, "Multi-Parametric Toolbox (MPT)," 2004, available from http://control. ee. ethz. ch/~mpt/.
23. J. M. Maciejowski, Predictive Control with Constraints. Prentice Hall, 2002.
24. D. Q. Mayne, "Constrained Optimal Control," European Control Conference, Plenary Lecture, Sept. 2001.
25. D. Q. Mayne and S. V. Rakovíc, "Model predictive control of constrained piecewise affine discrete-time systems," Int. Journal on Robust and Nonlinear Control, vol. 13, no. 3-4, pp. 261-279, 2003.
26. D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert, "Constrained model predictive control: Stability and optimality," Automatica, vol. 36, no. 6, pp. 789-814, June 2000.
27. J. Roll, A. Bemporad, and L. Ljung, "Identification of piecewise affine systems via mixed-integer programming," Automatica, vol. 40, pp. 37-50, 2004.
28. J. Snoeyink, "Point Location," in Handbook of Discrete and Computational Geometry, J. E. Goodman and J. O'Rouke, Eds. Boca Raton, New York: CRC Press, 1997, ch. 30, pp. 558-574.
29. E. D. Sontag, "Nonlinear regulation: The piecewise linear approach," IEEE Trans. on Automatic Control, vol. 26, no. 2, pp. 346-358, Apr. 1981.
30. P. Tøndel, T. A. Johansen, and A. Bemporad, "Evaluation of Piecewise Affine Control via Binary Search Tree," Automatica, vol. 39, no. 5, pp. 945-950, May 2003.
31. A. van der Schaft and H. Schumacher, An Introduction to Hybrid Dynamical Systems, ser. Lecture Notes in Control and Information Sciences. Springer-Verlag, 2000, vol. 251.