zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Decomposition principle in model predictive control for linear systems with bounded disturbances. (English) Zbl 1185.93024
Summary: Considering a constrained linear system with bounded disturbances, this paper proposes a novel approach which aims at enlarging the domain of attraction by combining a set-based Model Predictive Control (MPC) approach with a decomposition principle. The idea of the paper is to extend the “pre-stabilizing” MPC, where the MPC control sequence is parameterized as perturbation to a given pre-stabilizing feedback gain, to the case where the pre-stabilizing feedback law is given as the linear combination of a set of feedback gains. This procedure leads to a relatively large terminal set and consequently a large domain of attraction even when using short prediction horizons. As time evolves, by minimizing the nominal performance index, the resulting controller reaches the desired optimal controller with a good asymptotic performance. Compared to the standard “pre-stabilizing” MPC, it combines the advantages of having a flexible choice of feedback gains, a large domain of attraction and a good asymptotic behavior.

MSC:
93B11System structure simplification
93B40Computational methods in systems theory
93C05Linear control systems
93C73Perturbations in control systems
WorldCat.org
Full Text: DOI
References:
[1] Alamo, T.; Ramirez, D. R.; Camacho, E. F.: Efficient implementation of constrained MIN-MAX model predictive control with bounded uncertainties: A vertex rejection approach, Journal of process control, 149-158 (2005)
[2] Bacić, M.; Cannon, M.; Lee, Y. I.; Kouvaritakis, B.: General interpolation in MPC and its advantages, IEEE transactions on automatic control 48, 1092-1096 (2003)
[3] Boyd, S.; El Ghaoui, L.; Feron, E.; Balakrishnan, V.: Linear matrix inequalities in system and control theory, (1994) · Zbl 0816.93004
[4] Cannon, M.; Kouvaritakis, B.: Optimizing prediction dynamics for robust MPC, IEEE transactions on automatic control 50 (2005)
[5] Chisci, L.; Rossiter, J. A.; Zappa, G.: Systems with persistent disturbances: predictive control with restricted constraints, Automatica 37, 1019-1028 (2001) · Zbl 0984.93037 · doi:10.1016/S0005-1098(01)00051-6
[6] Imsland, L.; Rossiter, J. Anthony; Pluymers, Bert; Suykens, Johan: Robust triple mode MPC, American control conderence, 869-874 (2006)
[7] Keerthi, S. S.; Gilbert, E. G.: Computation of minimum-time feedback control laws for systems with state-control constraints, IEEE transactions on automatic control 32, 432-435 (1987) · Zbl 0611.93023 · doi:10.1109/TAC.1987.1104625
[8] Kerrigan, E. C.; Maciejowski, J. M.: Feedback MIN-MAX model predictive control using a single linear program: robust stability and the explicit solution, International journal of robust and nonlinear control 4, 395-413 (2004) · Zbl 1051.93034 · doi:10.1002/rnc.889
[9] Kolmanovsky, I.; Gilbert, E. G.: Theory and computation of disturbance invariance sets for discrecte-time linear systems, Mathematical probems in engineering: theory, methods and applications 4, 317-367 (1998) · Zbl 0923.93005 · doi:10.1155/S1024123X98000866
[10] Kouvaritakis, B.; Rossiter, J. A.; Schuurmans, J.: Efficient robust predictive control, IEEE transactions on automatic control 45, No. 8, 1545-1549 (2000) · Zbl 0988.93022 · doi:10.1109/9.871769
[11] Lee, J. H.; Yu, Z.: Worst case formulations of model predictive control for systems with bounded parameters, Automatica 33, 763-781 (1997) · Zbl 0878.93025 · doi:10.1016/S0005-1098(96)00255-5
[12] Mayne, D. Q.; Seron, M. M.; Raković, S. V.: Robust model predictive control of constrained linear systems with bounded disturbances, Automatica 41, 219-224 (2005) · Zbl 1066.93015 · doi:10.1016/j.automatica.2004.08.019
[13] Pluymers, B.; Roobrouck, L.; Buijs, J.; Suykens, J. A. K.; De Moor, B.: Constrained linear MPC with time-varying terminal cost using convex combinations, Automatica 41, 831-837 (2005) · Zbl 1093.93012 · doi:10.1016/j.automatica.2004.11.023
[14] Ramírez, D. R.; Camacho, E. F.: Piecewise affinity of MIN-MAX MPC with bounded additive uncertainties and a quadratic criterion, Automatica 42, 295-302 (2006) · Zbl 1099.93027 · doi:10.1016/j.automatica.2005.09.009
[15] Rossiter, J.A., Ding, Y., Pluymers, B., Suykens, J.A.K., & De Moor, B. Interpolation based MPC with exact constraint handling: The uncertain case. In European control conference ECC, 2005
[16] Rossiter, J. A.; Kouvaritakis, B.; Bacic, M.: Interpolation based computationally efficient predictive control, International journal of control 77, 290-301 (2004) · Zbl 1093.93013 · doi:10.1080/00207170310001655327
[17] Rossiter, J. A.; Kouvaritakis, B.; Rice, M. J.: A numerically robust state-space approach to stable predictive control strategies, Automatica 34, 65-73 (1998) · Zbl 0913.93022 · doi:10.1016/S0005-1098(97)00171-4
[18] Scokaert, P. O. M.; Mayne, D. Q.: MIN-MAX feedback model predictive control for constrained linear systems, IEEE transactions on automatic control 43, 1136-1142 (1998) · Zbl 0957.93034 · doi:10.1109/9.704989
[19] Sznaier, M., & Damborg, M. Suboptimal control of linear systems with state and control inequality constraints. In Proceedings 26th IEEE conference on decision and control, 1987 · Zbl 0713.93023
[20] Wan, Z. Y.; Kothare, M. V.: Efficient robust constrained model predictive control with a time-varying terminal constraint set, Systems and control letters 48, 375-383 (2003) · Zbl 1157.93395 · doi:10.1016/S0167-6911(02)00291-8