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)
Design of robust model-based controllers via parametric programming. (English) Zbl 1048.93033
Summary: In this paper a method is presented for deriving the explicit robust model-based optimal control law for constrained linear dynamic systems. The controller is derived off-line via parametric programming before any actual process implementation takes place. The proposed control scheme guarantees feasible operation in the presence of bounded input uncertainties by (i) explicitly incorporating in the controller design stage a set of feasibility constraints and (ii) minimizing the nominal performance, or the expectation of the performance over the uncertainty space. An extension of the method to problems involving target point tracking in the presence of persistent disturbances is also discussed. The general concept is illustrated with two examples.

MSC:
93B40Computational methods in systems theory
93B51Design techniques in systems theory
WorldCat.org
Full Text: DOI
References:
[1] Acevedo, J.; Pistikopoulos, E. N.: An algorithm for multiparametric mixed-integer linear programming problems. Operations research letters 24, 139-148 (1999) · Zbl 0941.90057
[2] Allwright, J.; Papavasiliou, G.: On linear programming and robust model-predictive control using impulse responses. Systems & control letters 18, 159-164 (1992) · Zbl 0756.90059
[3] Badgwell, T.: Robust model predictive control of stable linear systems. International journal of control 68, No. 4, 797-818 (1997) · Zbl 0889.93025
[4] Bemporad, A., Borelli, F., & Morari, M. (2001). Robust model predictive control: Piecewise linear explicit solution. In Proceedings of the European control conference, Porto, Portugal, pp. 939-944.
[5] Bemporad, A.; Borelli, F.; Morari, M.: MIN-MAX control of constrained uncertain discrete-time linear systems. Transactions of automatic control 48, No. 9, 1600-1606 (2003)
[6] Bemporad, A., & Morari, M. (1999). Robust model predictive control: A survey. In A. Garulli, A. Tesi & A. Vicino (Eds.), Robustness in identification and control (pp. 207-226). Berlin: Springer. · Zbl 0979.93518
[7] Bemporad, A.; Morari, M.; Dua, V.; Pistikopoulos, E. N.: The explicit linear quadratic regulator for constrained systems. Automatica 38, No. 1, 3-20 (2002) · Zbl 0999.93018
[8] Camacho, E.; Bordons, C.: Model predictive control. (1999) · Zbl 1223.93037
[9] Campo, P., & Morari, M. (1987). Robust model predictive control. In Proceedings of the American control conference, ACC, Minneapolis, pp. 1021-1026.
[10] Chmielewski, D.; Manousiouthakis, V.: On constrained infinite-time linear quadratic optimal control. Systems & control letters 29, 121-129 (1996) · Zbl 0867.49025
[11] Dua, V.; Bozinis, N. A.; Pistikopoulos, E. N.: A multiparametric programming approach for mixed integer and quadratic engineering problems. Computers & chemical engineering 26, No. 4-5, 715-733 (2002)
[12] Fiacco, A.: Introduction to sensitivity and stability analysis in nonlinear programming. (1983) · Zbl 0543.90075
[13] Grossmann, I.; Halemane, K.; Swaney, R.: Optimization strategies for flexible chemical processes. Computers & chemical engineering 7, No. 4, 439-462 (1983)
[14] Kothare, M.; Balakrishnan, V.; Morari, M.: Robust constrained model predictive control using linear matrix inequalities. Automatica 32, No. 10, 1361-1379 (1996) · Zbl 0897.93023
[15] Kwon, W.; Pearson, A.: A modified quadratic cost problem and feedback stabilization of a linear system. IEEE transactions on automatic control 22, No. 5, 838-842 (1977) · Zbl 0372.93037
[16] Lee, J., & Cooley, B. (1997). Recent advances in model predictive control and other related areas. In J. Kantor, C. Garcia, B. Carnahan (Eds.), Proceedings of chemical process control--V: Assessment and new directions for research. Vol. 93 of AIChe Symposium Series No. 316, AIChe and CACHE, pp. 201-216.
[17] Lee, J.; Cooley, B.: MIN-MAX predictive control techniques for linear state-space system with a bounded set of input matrices. Automatica 26, 463-473 (2000) · Zbl 1064.93509
[18] Lee, P.; Sullivan, G.: Generic model control (GMC). Computers & chemical engineering 12, No. 6, 573-580 (1988)
[19] Lee, J.; Yu, Z.: Worst-case formulations of model predictive control for systems with bounded parameters. Automatica 33, No. 5, 763-781 (1997) · Zbl 0878.93025
[20] Mayne, D.; Langson, W.: Robustifying model predictive control of constrained linear systems. Electronics letters 37, No. 23, 1422-1423 (2001)
[21] Mayne, D.; Rawlings, J.; Rao, C.; Scokaert, P.: Constrained model predictive controlstability and optimality. Automatica 36, 789-814 (2000) · Zbl 0949.93003
[22] Mayne, D.; Schroeder, W.: Robust time-optimal control of constrainted linear systems. Automatica 33, No. 12, 2103-2118 (1997) · Zbl 0910.93052
[23] Newell, R.; Lee, P.: Applied process control--A case study. (1989)
[24] Pistikopoulos, E. N., Bozinis, N. A., & Dua, V. (1999-2002). POP, a matlab implementation of parametric programming algorithms. Technical report, Centre for Process Systems Engineering, Imperial College, London, UK.
[25] Pistikopoulos, E. N.; Dua, V.; Bozinis, N. A.; Bemporad, A.; Morari, M.: On-line optimization via off-line parametric optimization tools. Computers & chemical engineering 26, No. 2, 175-185 (2002)
[26] Pistikopoulos, E. N.; Grossmann, I.: Optimal retrofit design for improving process flexibility in linear systems. Computers & chemical engineering 12, No. 7, 719-731 (1988)
[27] Ramirez, D., & Camacho, E. (2002). Characterization of min-max MPC with bounded uncertainties and quadratic criterion. In American control conference, Anchorage, Alaska, pp. 358-363.
[28] Rawlings, J.; Muske, K.: The stability of constrained receding horizon control. IEEE transactions on automatic control 38, No. 10, 1512-1516 (1993) · Zbl 0790.93019
[29] Sakizlis, V. (2003). Design of model based controllers via parametric programming. Ph.D. dissertation, Imperial College of Science, Technology and Medicine, London.
[30] Scokaert, P.; Mayne, D.: MIN-MAX feedback model predictive control for constrained linear systems. IEEE transactions on automatic control 43, No. 8, 1136-1142 (1998) · Zbl 0957.93034
[31] Scokaert, P.; Rawlings, J.: Constrained linear quadratic regulation. IEEE transactions on automatic control 43, No. 8, 1163-1169 (1998) · Zbl 0957.93033
[32] Zafiriou, E.: Robust model predictive control of processes with hard constraints. Computers & chemical engineering 14, No. 4/5, 359-371 (1990)