zbMATH — the first resource for mathematics

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.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
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)
Improving off-line approach to robust MPC based-on nominal performance cost. (English) Zbl 1140.93366
Summary: This paper gives two alternative off-line synthesis approaches to robust model predictive control (RMPC) for systems with polytopic description. In each approach, a sequence of explicit control laws that correspond to a sequence of nested asymptotically invariant ellipsoids are constructed off-line. In order to accommodate a wider class of systems, nominal performance cost is chosen to substitute the “worst-case” one in an existing technique. In the design of control law for a larger ellipsoid, the second approach further incorporates the knowledge of control laws associated with all smaller ellipsoids, so as to further improve feasibility and optimality. The effectiveness of the alternative approaches is illustrated by a simulation example.

93B51Design techniques in systems theory
93C55Discrete-time control systems
Full Text: DOI
[1] Angeli, D., Casavola, A., & Mosca, E. (2002). Ellipsoidal low-demanding MPC schemes for uncertain polytopic discrete-time systems. Proceedings of the 41st IEEE conference on decision and control, Las Vegas, Nevada USA (pp. 2935-2940).
[2] Cychowski, M. T., Ding, B., Tang, H., & O’Mahony, T. (2004). A new approach to off-line constrained robust model predictive control. Proceedings of the 2004 UK control conference (pp. 146).
[3] Gahinet, P., Nemirovski, A., Laub, A. J., & Chilali, M. (1995). LMI control toolbox for use with matlab, User’s guide. Natick, MA, USA: The Math Works Inc.
[4] Kothare, M. V.; Balakrishnan, V.; Morari, M.: Robust constrained model predictive control using linear matrix inequalities. Automatica 32, 1361-1379 (1996) · Zbl 0897.93023
[5] Kouvaritakis, B.; Rossiter, J. A.; Schuurmans, J.: Efficient robust predictive control. IEEE transactions on automatic control 45, 1545-1549 (2000) · Zbl 0988.93022
[6] Mayne, D. Q.; Rawlings, J. B.; Rao, C. V.; Scokaert, P. O. M.: Constrained model predictive control: stability and optimality. Automatica 36, 789-814 (2000) · Zbl 0949.93003
[7] Wan, Z.; 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
[8] Wan, Z.; Kothare, M. V.: An efficient off-line formulation of robust model predictive control using linear matrix inequalities. Automatica 39, 837-846 (2003) · Zbl 1032.93020