An SQP method for the optimal control of large-scale dynamical systems

被引：39

作者：

Gill, PE

Jay, LO

Leonard, MW

Petzold, LR ^{[1
]}

Sharma, V

机构：

[1] Univ Calif Santa Barbara, Dept Comp Sci, Santa Barbara, CA 93106 USA

[2] Univ Calif San Diego, Dept Math, La Jolla, CA 92093 USA

[3] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

[4] Univ Calif Los Angeles, Dept Math, Los Angeles, CA 90095 USA

[5] Univ Calif Santa Barbara, Dept Mech & Environm Engn, Santa Barbara, CA 93106 USA

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2000年 / 120卷 / 1-2期

基金：

美国国家科学基金会;

关键词：

multiple shooting; optimal control; sequential quadratic programming;

D O I：

10.1016/S0377-0427(00)00310-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We propose a sequential quadratic programming (SQP) method for the optimal control of large-scale dynamical systems. The method uses modified multiple shooting to discretize the dynamical constraints. When these systems have relatively few parameters, the computational complexity of the modified method is much less than that of standard multiple shooting. Moreover, the proposed method is demonstrably more robust than single shooting. In the context of the SQP method, the use of modified multiple shooting involves a transformation of the constraint Jacobian. The affected rows are those associated with the continuity constraints and any path constraints applied within the shooting intervals. Path constraints enforced at the shooting points (and other constraints involving only discretized states) are not transformed. The transformation is cast almost entirely at the user level and requires minimal changes to the optimization software. We show that the modified quadratic subproblem yields a descent direction for the l(1) penalty function. Numerical experiments verify the efficiency of the modified method. (C) 2000 Elsevier Science B.V. All rights reserved.

引用

页码：197 / 213

页数：17