Polynomial approximation of closed-form MPC for piecewise affine systems

IFAC Proceedings Volumes (IFAC-PapersOnline)

Volumn 17, Issue 1 PART 1, 2008, Pages

  Kvasnica, Michal ^a   Christophersen, Frank J ^a   Herceg, Martin ^a   Fikar, Miroslav ^a  

^a NONE

Author keywords

Control of switched systems; Parametric optimization; Sum of squares

Indexed keywords

CLOSED FORM; CLOSED LOOP STABILITY; CLOSED-FORM MODELS; CONSTRAINT SATISFACTION; CONTROLLER EVALUATION; HIGHER-DEGREE; OPTIMAL CONTROL LAW; PARAMETRIC OPTIMIZATION; PERFORMANCE DECAY; PIECEWISE AFFINE SYSTEMS; PRACTICAL IMPLEMENTATION; SHORT SAMPLING; STATE SPACE; SUM-OF-SQUARES;

ELECTRIC NETWORK PARAMETERS; MODEL PREDICTIVE CONTROL; OPTIMIZATION; POLYNOMIAL APPROXIMATION; PREDICTIVE CONTROL SYSTEMS; SWITCHING SYSTEMS;

CONTROLLERS;

EID: 79961019364     PISSN: 14746670     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.3182/20080706-5-KR-1001.1470     Document Type: Conference Paper

References (18)

1. 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.
2. A. Bemporad and M. Morari. Control of systems integrating logic, dynamics, and constraints. Automatica, 35(3):407-427, March 1999.
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. J. Eve. The Evaluation of Polynomials. Numerische Mathematik, 6:17-21, 1964.
6. 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.
7. W. P. M. H. Heemels, B. De Schutter, and A. Bemporad. Equivalence of hybrid dynamical models. Automatica, 37(7):1085-1091, 2001.
8. M. Kvasnica, P. Grieder, and M. Baotic. Multi-Parametric Toolbox (MPT), 2004. Available from http://control.ee.ethz.ch/~mpt/.
9. M. Lazar, W. P. M. H. Heemels, B. J. P. Roset, H. Nijmeijer, and P. P. J. van den Bosch. Input-to-state stabilizing sub-optimal nmpc with an application to dc-dc converters. International Journal of Robust and Nonlinear Control, 9999(9999):n/a+, 2007. doi: 10.1002/rnc.1249.
10. 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. doi: 10.1016/j.sysconle.2007.06.013. (Pubitemid 350087248)
11. J. Lofberg. YALMIP : A Toolbox for Modeling and Optimization in MATLAB. In Proc. of the CACSD Conference, Taipei, Taiwan, 2004. Available from http://control.ee.ethz.ch/~joloef/yalmip.php.
12. 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.
13. P. A. Parrilo. Sums of squares of polynomials and their applications. In ISSAC '04: Proceedings of the 2004 international symposium on Symbolic and algebraic computation, pages 1-1, New York, NY, USA, 2004.
14. E. D. Sontag. Nonlinear regulation: The piecewise linear approach. IEEE Trans. on Automatic Control, 26(2):346-358, April 1981.
15. G. Stengle. A Nullstellensatz and a Positivstellensatz in semialgebraic geometry . Math. Ann., 207:87-97, 1974.
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. A. Ulbig, S. Olaru, D. Dumur, and P. Boucher. Explicit solutions for nonlinear model predictive control: A linear mapping approach. In S. G. Tzafestas and P. J. Antsaklis, editors, Proc. of of the European Control Conference 2007, pages 3295-3302, 2007.
18. M. Vidyasagar. Nonlinear Systems Analysis. Prentice Hall, 2nd edition, 1993.