A logarithmic-time solution to the point location problem for parametric linear programming

Automatica

Volumn 42, Issue 12, 2006, Pages 2215-2218

  Jones, C N ^a   Grieder, P ^b   Rakovic S V ^c  

^a UNIVERSITY OF CAMBRIDGE   (United Kingdom)

^b ETH ZURICH   (Switzerland)

^c IMPERIAL COLLEGE LONDON   (United Kingdom)

Author keywords

Controller complexity; Parametric programming; Predictive control

Indexed keywords

OPTIMAL CONTROL SYSTEMS; OPTIMIZATION; PARAMETER ESTIMATION; PREDICTIVE CONTROL SYSTEMS; PROBLEM SOLVING;

CONTROLLER COMPLEXITY; LOGARITHMIC TIME SOLUTION; PARAMETRIC LINEAR PROGRAM (PLP); PARAMETRIC LINEAR PROGRAMMING; POINT LOCATION PROBLEM;

LINEAR PROGRAMMING;

EID: 33750462380     PISSN: 00051098     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.automatica.2006.07.010     Document Type: Article

References (12)

1. Arya S., Mount D.M., Netanyahu N.S., Silverman R., and Wu A.Y. An optimal algorithm for approximate nearest neighbor searching fixed dimensions. Journal of the ACM 45 6 (1998) 891-923
2. Aurenhammer F. Voronoi diagrams-a survey of a fundamental geometric data structure. ACM Computing Surveys 23 3 (1991)
3. Bemporad A., Morari M., Dua V., and Pistikopoulos E.N. The explicit linear quadratic regulator for constrained systems. Automatica 38 1 (2002) 3-20
4. Borrelli, F. (2003). Constrained optimal control of linear and hybrid systems, Lecture notes in control and information sciences (Vol. 290). Berlin: Springer.
5. Borelli, F., Baotić, M., Bemporad, A., & Morari, M. (2001). Efficient on-line computation of constrained optimal control. Proceedings of the 40th IEEE conference on decision and control (pp. 1187-1192). Orlando, Florida.
6. Grünbaum B. Convex polytopes. 2nd ed. (2000), Springer, Berlin
7. Jones, C. N. (2005). Polyhedral tools for control. Ph.D. thesis, University of Cambridge, 2005.
8. Kvasnica, M., Grieder, P., Baotić, M., & Morari, M. (2003). Multi parametric toolbox (MPT). In Hybrid systems: Computation and control, Lecture Notes in Computer Science. Berlin: Springer.
9. Mount, D., & Arya, S. (1998). ANN: Library for approximate nearest neighbor searching.
10. Raković, S. V., Grieder, P., & Jones, C. (2004). Computation of Voronoi diagrams and delaunay triangulation via parametric linear programming. Technical Report AUT04-03, Automatic Control Lab, ETHZ, Switzerland.
11. Tøndel P., Johansen T.A., and Bemporad A. An algorithm for multi-arametric quadratic programming and explicit MPC solutions. Automatica 39 3 (2003) 489-497
12. Tøndel P., Johansen T.A., and Bemporad A. Computation of piecewise affine control via binary search tree. Automatica 39 5 (2003) 945-950