Computcation of the constrained infinite time linear quadratic regulator

被引：85

作者：

Grieder, P ^{[1
]}

Borrelli, F ^{[1
]}

Torrisi, F ^{[1
]}

Morari, M ^{[1
]}

机构：

[1] ETH, Swiss Fed Inst Technol, Inst Automat, CH-8092 Zurich, Switzerland

来源：

AUTOMATICA | 2004年 / 40卷 / 04期

关键词：

constrained infinite horizon control; linear quadratic regulator; model predictive control; invariant set;

D O I：

10.1016/j.automatica.2003.11.014

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

This paper presents an efficient algorithm for computing the solution to the constrained infinite-time, linear quadratic regulator (CLQR) problem for discrete time systems. The algorithm combines multi-parametric quadratic programming with reachability analysis to obtain the optimal piecewise affine (PWA) feedback law. The algorithm reduces the time necessary to compute the PWA solution for the CLQR when compared to other approaches. It also determines the minimal finite horizon (N) over bar (J), such that the constrained finite horizon LQR problem equals the CLQR problem for a compact set of states J. The on-line computational effort for the implementation of the CLQR can be significantly reduced as well, either by evaluating the PWA solution or by solving the finite dimensional quadratic program associated with the CLQR for a horizon of N = (N) over bar (J). (C) 2003 Elsevier Ltd. All rights reserved.

引用

页码：701 / 708

页数：8

共 16 条

[1] BAOTIC M, 2002, AUT0204 ETH ZUR
[2] The explicit linear quadratic regulator for constrained systems
Bemporad, A
Morari, M
Dua, V
Pistikopoulos, EN
[J]. AUTOMATICA, 2002, 38 (01) : 3 - 20
[3] Convexity recognition of the union of polyhedra
Bemporad, A
Fukuda, K
Torrisi, FD
[J]. COMPUTATIONAL GEOMETRY-THEORY AND APPLICATIONS, 2001, 18 (03): : 141 - 154
[4] BORRELLI F, 2001, P 10 IEEE C DEC CONT
[5] BORRELLI F, 2003, LECT NOTES CONTROL I, V290
[6] Fast algorithm for a constrained infinite horizon LQ problem
Chisci, L
Zappa, G
[J]. INTERNATIONAL JOURNAL OF CONTROL, 1999, 72 (11) : 1020 - 1026
[7] On constrained infinite-time linear quadratic optimal control
Chmielewski, D
Manousiouthakis, V
[J]. SYSTEMS & CONTROL LETTERS, 1996, 29 (03) : 121 - 129
[8] CUTTLER CR, 1980, P AM CONTR C WP B, V5
[9] GEVERS M, 1990, ADAPTIVE OPTIMAL CON
[10] LINEAR-SYSTEMS WITH STATE AND CONTROL CONSTRAINTS - THE THEORY AND APPLICATION OF MAXIMAL OUTPUT ADMISSIBLE-SETS
GILBERT, EG
TAN, KT
[J]. IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1991, 36 (09) : 1008 - 1020

← 1 2 →