Set Membership approximation theory for fast implementation of Model Predictive Control laws

Automatica

Volumn 45, Issue 1, 2009, Pages 45-54

  Canale, M ^a   Fagiano, L ^a   Milanese, M ^a  

^a POLITECNICO DI TORINO   (Italy)

Author keywords

Constraint satisfaction; Function approximation; Nonlinear systems analysis; Predictive control

Indexed keywords

APPROXIMATION THEORY; FUNCTIONS; LAWS AND LEGISLATION; LINEAR SYSTEMS; NONLINEAR SYSTEMS; POLYNOMIAL APPROXIMATION; PREDICTIVE CONTROL SYSTEMS; PROBABILITY DENSITY FUNCTION; STEELMAKING; SYSTEMS ANALYSIS;

APPROXIMATING FUNCTIONS; APPROXIMATION ERRORS; APPROXIMATION TECHNIQUES; BOUNDEDNESS; COMPACT SETS; COMPUTATIONAL TIMES; CONSTRAINT SATISFACTION; CONVERGENCY; EXACT CONTROLS; FAST IMPLEMENTATIONS; FINITE NUMBERS; FUNCTION APPROXIMATION; GUARANTEED PERFORMANCES; INPUT CONSTRAINTS; LOOP STABILITIES; NUMERICAL EXAMPLES; PREDICTIVE CONTROL; PREDICTIVE CONTROL LAWS; STATE CONSTRAINTS; STATE TRAJECTORIES;

MODEL PREDICTIVE CONTROL;

EID: 57949094425     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2008.06.015     Document Type: Article

References (25)

1. Alamir M. Stabilization of nonlinear systems by receding-horizon control schemes: Parametrized approach for fast systems (2006), Springer
2. Bemporad A., and Filippi C. Suboptimal explicit receding horizon control via approximate multiparametric quadratic programming. Journal of Optimization Theory and Applications (2003)
3. Bemporad A., and Filippi C. An algorithm for approximate multiparametric convex programming. Computational Optimization and Applications 35 (2006) 87-108
4. Bemporad A., Morari M., Dua V., and Pistikopoulos E.N. The explicit linear quadratic regulator for constrained systems. Automatica 38 (2002) 3-20
5. Blagovest, Ch S. Hausdorff approximations (1990), Springer
6. Borrelli F., Baotić M., Bemporad A., and Morari M. Dynamic programming for constrained optimal control of discrete-time linear hybrid systems. Automatica 41 (2005) 1709-1721
7. Canale, M., & Milanese, M. (2005). FMPC: A fast implementation of model predictive control. In 16th IFAC world congress
8. Canale M., Fagiano L., and Milanese M. Power kites for wind energy generation. IEEE Control Systems Magazine 27 6 (2007) 25-38
9. Canale M., Milanese M., and Novara C. Semi-active suspension control using fast model-predictive techniques. IEEE Transactions on Control System Technology 14 6 (2006) 1034-1046
10. Diehl M., and Björnberg J. Robust dynamic programming for min-max model predictive control of constrained uncertain systems. IEEE Transactions on Automatic Control 49 12 (2004) 2253-2257
11. Goodwin G.C., Seron M., and De Dona J. Constrained control and estimation: An Optimisation approach (2005), Springer
12. Johansen T.A. Approximate explicit receding horizon control of constrained nonlinear systems. Automatica 40 (2004) 293-300
13. Johansen T.A., and Grancharova A. Approximate explicit constrained linear model predictive control via orthogonal search tree. IEEE Transactions on Automatic Control 48 5 (2003) 810-815
14. Johansen T.A., Petersen I., and Slupphaug O. Explicit suboptimal linear quadratic regulation with state and input constraints. Automatica 38 (2002) 1099-1111
15. Kvasnica, M., Grieder, P., & Christophersen, F. J. (2006). Multi-parametric toolbox - ver. 2.6.2. http://control.ee.ethz.ch/~mpt
16. Mayne D.Q., Rawlings J.B., Rao C.V., and Scokaert P.O.M. Constrained model predictive control: Stability and optimality. Automatica 36 (2000) 789-814
17. Milanese M., and Novara C. Set membership identification of nonlinear systems. Automatica 40 (2004) 957-975
18. MOSEK ApS (2006). Mosek optimization toolbox - ver. 4.0. http://www.mosek.com
19. Parisini T., and Zoppoli R. A receding-horizon regulator for nonlinear systems and a neural approximation. Automatica 31 10 (1995) 1443-1451
20. Polak E., and Yang T.H. Moving horizon control of linear systems with input saturation and plant uncertainty-part 1: Robustness. International Journal of Control 58 3 (1993) 613-638
21. Seron M.M., Goodwin G.C., and De Doná J.A. Characterization of receding horizon control for constrained linear systems. Asian Journal of Control 5 2 (2003) 271-286
22. Spjøtvold J., Tøndel P., and Johansen T.A. Continuous selection and unique polyhedral representation of solutions to convex parametric quadratic programs. Journal of Optimization Theory and Applications 134 (2007) 177-189
23. Tondel, P., Johansen, T. A., & Bemporad, A. (2002). Computation and approximation of piecewise linear affine control laws via binary search trees. In 41st IEEE conference decision an control (pp. 3144-3149)
24. Wang L., Heng P.A., and Leung K.S. Global exponential asymptotic stability in nonlinear discrete dynamical systems. Journal of Mathematical Analysis and Applications 258 1 (2001) 349-358
25. Zheng A., Kothare M.V., and Morari M. Anti-windup design for internal model control. International Journal of Control 60 5 (1994) 1015-1022