Low-complexity polynomial approximation of explicit MPC via linear programming

Proceedings of the 2010 American Control Conference, ACC 2010

Volumn , Issue , 2010, Pages 4713-4718

  Kvasnica, Michal ^b   Löfberg, Johan ^a   Herceg, Martin ^b   Čirka, L'Uboš ^b   Fikar, Miroslav ^b  

^a LINKÖPING UNIVERSITY   (Sweden)

^b SLOVAK UNIVERSITY OF TECHNOLOGY   (Slovakia)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINT SATISFACTION PROBLEMS; LINEAR PROGRAMMING; PREDICTIVE CONTROL SYSTEMS; STATE FEEDBACK;

CLOSED LOOP STABILITY; CONSTRAINT SATISFACTION; EXPLICIT SOLUTIONS; LINEAR PROGRAMS; MODEL PREDICTIVE CONTROLLERS; OPTIMAL CONTROL LAW; PERFORMANCE DECAY; SINGLE POLYNOMIALS;

POLYNOMIAL APPROXIMATION;

EID: 77957806210     PISSN: None     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1109/acc.2010.5531092     Document Type: Conference Paper

References (18)

1. M. Baotić, F. J. Christophersen, and M. Morari. Constrained Optimal Control of Hybrid Systems With a Linear Performance Index. IEEE Trans. on Automatic Control, 51(12):1903-1919, December 2006. (Pubitemid 46002284)
2. A. Bemporad and C. Filippi. Suboptimal explicit RHC via approximate multiparametric quadratic programming. Journal of Optimization Theory and Applications, 117(1):9-38, April 2003.
3. F. Borrelli. Constrained Optimal Control of Linear and Hybrid Systems, volume 290 of Lecture Notes in Control and Information Sciences. Springer-Verlag, 2003.
4. F. J. Christophersen. Optimal Control of Constrained Piecewise Affine Systems, volume 359 of Lecture Notes in Control and Information Sciences. Springer Verlag, 2007.
5. T. Geyer, F. D. Torrisi, and M. Morari. Optimal Complexity Reduction of Piecewise Affine Models Based on Hyperplane Arrangements. In Proc. on the American Control Conference, pages 1190-1195, Boston, Massachusetts, USA, June 2004.
6. G. H. Hardy, J. E. Littlewood, and G. Ṕolya. Inequalities. Cambridge University Press, second edition, 1952.
7. M. Huba, P. Kurčík, and M. Kamenský. Thermo-optical device uDAQ28/LT. STU Bratislava, Illkovičova 3, Bratislava, 2006. In Slovak.
8. ILOG, Inc. CPLEX User Manual. Gentilly Cedex, France. http://www.ilog.fr/products/cplex/.
9. M. Kvasnica, F. J. Christophersen, M. Herceg, and M. Fikar. Polynomial approximation of closed-form MPC for piecewise affine systems. In Proceedings of the 17th IFAC World Congress, pages 3877-3882, Seoul, Korea, July 6-11 2008.
10. M. Kvasnica, P. Grieder, M. Baotic, and M. Morari. Multi-Parametric Toolbox (MPT). In Hybrid Systems: Computation and Control, pages 448-462, March 2004.
11. M. Lazar, D. Munoz de la Pena, W.P.M.H. Heemels, and T. Alamo. On input-to-state stability of min-max nonlinear model predictive control. Systems & Control Letters, 57:39-48, 2008.
12. M. Lazar, W. P. M. H. Heemels, B. J. P. Roset, H. Nijmeijer, and P. P. J. van den Bosch. Input-to-state stabilizing suboptimal nmpc with an application to dc-dc converters. International Journal of Robust and Nonlinear Control, 2007.
13. J. Löfberg. Yalmip : A toolbox for modeling and optimization in MATLAB. In Proceedings of the CACSD Conference, Taipei, Taiwan, 2004.
14. D. Q. Mayne, J. B. Rawlings, C. V. Rao, and P. O. M. Scokaert. Constrained model predictive control: Stability and optimality. Automatica, 36(6):789-814, June 2000.
15. K.C. Toh, M.J. Todd, and R.H. Tütüncü. SDPT3 - a Matlab software package for semidefinite programming. Optimization Methods and Software, 11/12:545-581, 1999.
16. P. Tøndel, T. A. Johansen, and A. Bemporad. Evaluation of Piecewise Affine Control via Binary Search Tree. Automatica, 39(5):945-950, May 2003.
17. M. Vidyasagar. Nonlinear Systems Analysis. Prentice Hall, 2nd edition, 1993.
18. L'. Čirka., M. Fikar, and P. Petruš. IDTOOL 4.0 - A Dynamical System Identification Toolbox for MATLAB/Simulink. In 14th Annual Conference Proceedings: Technical Computing Prague 2006, pages 29-29, October 2006.