Synthesis of stabilizing model predictive controllers via canonical piecewise affine approximations

Proceedings of the IEEE Conference on Decision and Control

Volumn , Issue , 2010, Pages 5296-5301

  Bemporad, Alberto ^a   Oliveri, Alberto ^b   Poggi, Tomaso ^b   Storace, Marco ^b  

^a UNIVERSITY OF TRENTO   (Italy)

^b UNIVERSITY OF GENOA   (Italy)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; CLOSED LOOP SYSTEMS; LYAPUNOV FUNCTIONS; PREDICTIVE CONTROL SYSTEMS;

ANALYSIS TOOLS; CONTROLLER SYNTHESIS; MODEL PREDICTIVE CONTROLLERS; ON CHIPS; PIECEWISE AFFINE APPROXIMATION; PIECEWISE AFFINE FUNCTIONS; SAMPLING TIME;

CONTROLLERS;

EID: 79953135833     PISSN: 07431546     EISSN: 25762370     Source Type: Conference Proceeding    
DOI: 10.1109/CDC.2010.5717868     Document Type: Conference Paper

References (30)

1. E. Camacho and C. Bordons, Model Predictive Control, 2nd ed., ser. Advanced Textbooks in Control and Signal Processing. London: Springer-Verlag, 2004.
2. J. Maciejowski, Predictive Control with Constraints. Harlow, UK: Prentice Hall, 2002.
3. A. Alessio and A. Bemporad, "A survey on explicit model predictive control," in Nonlinear Model Predictive Control: Towards New Challenging Applications, ser. Lecture Notes in Control and Information Sciences, D. R. L. Magni, F. Allgower, Ed., vol. 384. Berlin Heidelberg: Springer-Verlag, 2009, pp. 345-369.
4. S. Di Cairano, D. Yanakiev, A. Bemporad, I. Kolmanovsky, and D. Hrovat, "An MPC design flow for automotive control and applications to idle speed regulation," in Proc. 47th IEEE Conf. on Decision and Control, Cancun, Mexico, 2008, pp. 5686-5691.
5. A. Beccuti, G. Papafotiou, R. Frasca, and M. Morari, "Explicit hybrid model predictive control of the DC-DC boost converter," in IEEE PESC, Orlando, Florida, USA, June 2007.
6. A. Bemporad and C. Filippi, "Suboptimal explicit receding horizon control via approximate multiparametric quadratic programming," Journal of Optimization Theory and Applications, vol. 117, no. 1, pp. 9-38, Apr. 2003.
7. C. Jones, M. Baric, and M. Morari, "Multiparametric linear programming with applications to control," European Journal of Control, vol. 13, pp. 152-170, 2007.
8. T. Johansen and A. Grancharova, "Approximate explicit constrained linear model predictive control via orthogonal search tree," IEEE Trans. Automatic Control, vol. 58, no. 5, pp. 810-815, May 2003.
9. D. Muñoz de la Peña, A. Bemporad, and C. Filippi, "Robust explicit MPC based on approximate multi-parametric convex programming," IEEE Trans. Automatic Control, vol. 51, no. 8, pp. 1399-1403, Aug. 2006.
10. T. Parisini and R. Zoppoli, "A receding-horizon regulator for nonlinear systems and a neural approximation," Automatica, vol. 31, no. 10, pp. 1443-1451, 1995.
11. M. Canale, L. Fagiano, and M. Milanese, "Set membership approximation theory for fast implementation of model predictive control," Automatica, vol. 45, no. 1, pp. 45-54, 2009.
12. P. Julián, A. Desages, and O. Agamennoni, "High-level canonical piecewise linear representation using a simplicial partition," IEEE Transactions on Circuits and Systems I, vol. 46, no. 4, pp. 463-480, Apr. 1999.
13. M. Storace and T. Poggi, "Digital architectures realizing piecewiselinear multi-variate functions: two FPGA implementations," International Journal of Circuit Theory and Applications, vol. 37, 2010, in the press (doi: 10.1002/cta.610).
14. M. Di Federico, T. Poggi, P. Julian, and M. Storace, "Integrated circuit implementation of multi-dimensional piecewise-linear functions," Digital Signal Processing, vol. 20, 2010.
15. 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.
16. A. Bemporad, M. Morari, and N. Ricker, Model Predictive Control Toolbox for Matlab - User's Guide. The Mathworks, Inc., 2004, http://www.mathworks.com/ access/helpdesk/help/toolbox/mpc/.
17. A. Bemporad, Hybrid Toolbox - User's Guide, Jan. 2004, http://www. dii.unisi.it/hybrid/toolbox.
18. T. Johansen, W. Jackson, R. Schrieber, and P. Tøndel, "Hardware synthesis of explicit model predictive controllers," IEEE Trans. Contr. Systems Technology, vol. 15, no. 1, pp. 191-197, 2007.
19. A. Oliveri, A. Oliveri, T. Poggi, and M. Storace, "Circuit implementation of piecewise-affine functions based on a binary search tree," in Proceedings of ECCTD'09, Antalya, Turkey, Aug. 2009, pp. 145-148.
20. C. Filippi, "An algorithm for approximate multiparametric linear programming," Journal of Optimization Theory and Applications, vol. 120, no. 1, pp. 73-95, 2004.
21. H. Kuhn, "Some combinatorial lemmas in topology," IBM J. of Research and Development, vol. 4, pp. 518-524, 1960.
22. P. Julián, A. Desages, and B. D'Amico, "Orthonormal high level canonical PWL functions with applications to model reduction," IEEE Transactions on Circuits and Systems I, vol. 47, no. 5, pp. 702-712, May 2000.
23. R. Rovatti, M. Borgatti, and R. Guerrieri, "A geometric approach to maximum-speed n-dimensional continuous linear interpolation in rectangular grids," IEEE Transactions on Computers, vol. 47, no. 8, pp. 894-899, AUG 1998.
24. R. Rovatti, C. Fantuzzi, and S. Simani, "High-speed DSP-based implementation of piecewise-affine and piecewise-quadratic fuzzy systems," Signal Processing, vol. 80, pp. 951-963, 2000.
25. P. Echevarria, M. Martínez, J. Echanobe, I. del Campo, and J. Tarela, "Digital hardware implementation of high dimensional fuzzy systems," in Applications of Fuzzy Sets Theory, ser. Lecture Notes in Computer Science. Berlin: Springer, 2007, pp. 245-252.
26. F. Blanchini, "Ultimate boundedness control for uncertain discretetime systems via set-induced Lyapunov functions," IEEE Trans. Automatic Control, vol. 39, no. 2, pp. 428-433, Feb. 1994.
27. A. Alessio, M. Lazar, A. Bemporad, and W. Heemels, "Squaring the circle: An algorithm for generating polyhedral invariant sets from ellipsoidal ones," Automatica, vol. 43, pp. 2096-2103, Dec. 2007.
28. A. Bemporad, A. Oliveri, T. Poggi, and M. Storace, "Ultra-fast stabilizing model predictive control via canonical piecewise affine approximations," 2010, internal report, submitted for publication. Available upon request from the authors.
29. G. Ferrari-Trecate, F. Cuzzola, D. Mignone, and M. Morari, "Analysis of discrete-time piecewise affine and hybrid systems," Automatica, vol. 38, pp. 2139-2146, 2002.
30. J. Löfberg, "YALMIP: A toolbox for modeling and optimization in MATLAB," in Proceedings of the CACSD Conference, Taipei, Taiwan, 2004. [Online]. Available: http://users.isy.liu.se/johanl/yalmip