# 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)
Efficient robust constrained model predictive control with a time varying terminal constraint set. (English) Zbl 1157.93395
Summary: An efficient robust constrained model predictive control algorithm with a time varying terminal constraint set is developed for systems with model uncertainty and input constraints. The approach is novel in that it off-line constructs a continuum of terminal constraint sets and on-line achieves robust stability by using a relatively short control horizon (even $N=0$) with a time varying terminal constraint set. This algorithm not only dramatically reduces the on-line computation but also significantly enlarges the size of the allowable set of initial conditions. Moreover, this control scheme retains the unconstrained optimal performance in the neighborhood of the equilibrium. The controller design is illustrated through a benchmark problem.

##### MSC:
 93B51 Design techniques in systems theory 49N90 Applications of optimal control and differential games
LMI toolbox
Full Text:
##### References:
 [1] Broom, A. C.; Kouvaritakis, B.; Lee, Y. I.: Constrained MPC for uncertain linear systems with ellipsoidal target sets. Systems control lett. 44, 157-166 (2001) · Zbl 1103.93361 [2] Casavola, A.; Giannelli, M.; Mosca, E.: MIN--MAX predictive control strategies for input-saturated polytopic uncertain systems. Automatica 36, No. 1, 125-133 (2000) · Zbl 0939.93506 [3] Cuzzola, F. A.; Geromel, J. C.; Morari, M.: An improved approach for constrained robust model predictive control. Automatica 38, No. 7, 1183-1189 (2002) · Zbl 1010.93042 [4] Gahinet, P.; Nemirovski, A.; Laub, A. J.; Chilali, M.: LMI control toolbox: for use with Matlab. (May 1995) [5] Kothare, M. V.; Balakrishnan, V.; Moraŕi, M.: Robust constrained model predictive control using linear matrix inequalities. Automatica 32, No. 10, 1361-1379 (1996) · Zbl 0897.93023 [6] Kouvaritakis, B.; Rossiter, J. A.; Schuurmans, J.: Efficient robust predictive control. IEEE trans. Automat. control 45, No. 8, 1545-1549 (2000) · Zbl 0988.93022 [7] Lee, Y. I.; Kouvaritakis, B.: A linear programming approach to constrained robust predictive control. IEEE trans. Automat. control 45, No. 9, 1765-1770 (2000) · Zbl 0990.93116 [8] Magni, L.; De Nicolao, G.; Magnani, L.; Scattolini, R.: A stabilizing model-based predictive control algorithm for nonlinear systems. Automatica 37, 1351-1362 (2001) · Zbl 0995.93033 [9] Mayne, D. Q.; Rawlings, J. B.; Rao, C. V.; Scokaert, P. O. M.: Constrained model predictive controlstability and optimality. Automatica 36, No. 6, 789-814 (2000) · Zbl 0949.93003 [10] Wie, B.; Bernstein, D. S.: Benchmark problems for robust control design. J. guidance, control, dynamics 15, No. 5, 1057-1059 (1992) [11] Wredenhagen, G. F.; Belanger, P. R.: Piecewise-linear LQ control for systems with input constraints. Automatica 30, No. 3, 403-416 (1994) · Zbl 0800.93519