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Optimal Control of Systems Described by Index Two Differential-Algebraic Equations

Authors:

C. C. Pantelides,

R. W. H. SargentAuthors Info & Claims

SIAM Journal on Scientific Computing, Volume 16, Issue 6

Pages 1349 - 1366

https://doi.org/10.1137/0916078

Published: 01 November 1995 Publication History

Abstract

The optimal control problems considered here seek to determine a time-varying control action and a set of time-invariant parameters that optimize the performance of a dynamic system whose behaviour is described by index two differential-algebraic equations (DAEs).

The problem formulation accommodates equality and inequality end and interior point constraints as well as constraints on control variables and parameters. The control parameterization approach, whereby the original problem is transformed into a nonlinear programming problem, is adopted.

Due to the features of index two DAEs, the control representation employed may yield a discontinuous system trajectory and for this reason it is necessary to define functions yielding consistent initial conditions following control variable discontinuities. Variational analysis is carried out to derive expressions for the objective and constraint function gradients with respect to the optimization decision variables. A key characteristic of this analysis is that, in addition to the original equations, it is necessary to adjoin equations resulting from manipulation of the original algebraic equations and their time derivatives.

References

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Kenneth D. Clark, Linda R. Petzold, Numerical solution of boundary value problems in differential-algebraic systems, SIAM J. Sci. Statist. Comput., 10 (1989), 915–936

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Cited By

Gerdts MKunkel M(2011)A globally convergent semi-smooth Newton method for control-state constrained DAE optimal control problemsComputational Optimization and Applications10.1007/s10589-009-9275-048:3(601-633)Online publication date: 1-Apr-2011
https://dl.acm.org/doi/10.1007/s10589-009-9275-0

Index Terms

Optimal Control of Systems Described by Index Two Differential-Algebraic Equations
1. Mathematics of computing
  1. Mathematical analysis
    1. Mathematical optimization
2. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization

Index terms have been assigned to the content through auto-classification.

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Published In

cover image SIAM Journal on Scientific Computing

SIAM Journal on Scientific Computing Volume 16, Issue 6

Nov 1995

271 pages

ISSN:1064-8275

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Copyright © 1995 Society for Industrial and Applied Mathematics.

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Society for Industrial and Applied Mathematics

United States

Publication History

Published: 01 November 1995

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Cited By

Gerdts MKunkel M(2011)A globally convergent semi-smooth Newton method for control-state constrained DAE optimal control problemsComputational Optimization and Applications10.1007/s10589-009-9275-048:3(601-633)Online publication date: 1-Apr-2011
https://dl.acm.org/doi/10.1007/s10589-009-9275-0

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