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

Philip E Gill; Laurent O Jay; Michael W Leonard; Linda R Petzold; Vivek Sharma

doi:10.1016/S0377-0427(00)00310-1

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

Journal article

Open access

Peer reviewed

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

Philip E Gill, Laurent O Jay, Michael W Leonard, Linda R Petzold and Vivek Sharma

Journal of computational and applied mathematics, Vol.120(1), pp.197-213

2000

DOI: 10.1016/S0377-0427(00)00310-1

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Abstract

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.

Sequential quadratic programming

Multiple shooting

Optimal control

Details

Title: Subtitle: An SQP method for the optimal control of large-scale dynamical systems
Creators: Philip E Gill - Department of Mathematics, University of California, San Diego, La Jolla, CA 92093-0112, USA
Laurent O Jay - Department of Mathematics, The University of Iowa, Iowa City, IA 52242-1419, USA
Michael W Leonard - Department of Mathematics, University of California, Los Angeles, CA 90095-1555, USA
Linda R Petzold - Department of Computer Science, and Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, CA 93106-5070, USA
Vivek Sharma - Department of Computer Science, and Department of Mechanical and Environmental Engineering, University of California, Santa Barbara, CA 93106-5070, USA
Resource Type: Journal article
Publication Details: Journal of computational and applied mathematics, Vol.120(1), pp.197-213
DOI: 10.1016/S0377-0427(00)00310-1
ISSN: 0377-0427
eISSN: 1879-1778
Publisher: Elsevier B.V
Language: English
Date published: 2000
Academic Unit: Mathematics
Record Identifier: 9983985831702771

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