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Local Minimum Principle for Optimal Control Problems Subject to Differential-Algebraic Equations of Index Two

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  • M. Gerdts

    (University of Hamburg)

Abstract

Necessary conditions in terms of a local minimum principle are derived for optimal control problems subject to index-2 differential-algebraic equations, pure state constraints, and mixed control-state constraints. Differential-algebraic equations are composite systems of differential equations and algebraic equations, which arise frequently in practical applications. The local minimum principle is based on the necessary optimality conditions for general infinite optimization problems. The special structure of the optimal control problem under consideration is exploited and allows us to obtain more regular representations for the multipliers involved. An additional Mangasarian-Fromowitz-like constraint qualification for the optimal control problem ensures the regularity of a local minimum. An illustrative example completes the article.

Suggested Citation

  • M. Gerdts, 2006. "Local Minimum Principle for Optimal Control Problems Subject to Differential-Algebraic Equations of Index Two," Journal of Optimization Theory and Applications, Springer, vol. 130(3), pages 443-462, September.
    • Handle: RePEc:spr:joptap:v:130:y:2006:i:3:d:10.1007_s10957-006-9121-9
    DOI: 10.1007/s10957-006-9121-9
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    References listed on IDEAS

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    1. M. Gerdts, 2003. "Direct Shooting Method for the Numerical Solution of Higher-Index DAE Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 117(2), pages 267-294, May.
    2. K. Malanowski & H. Maurer & S. Pickenhain, 2004. "Second-Order Sufficient Conditions for State-Constrained Optimal Control Problems," Journal of Optimization Theory and Applications, Springer, vol. 123(3), pages 595-617, December.
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    Cited by:

    1. Matthias Gerdts & Björn Hüpping, 2012. "Virtual control regularization of state constrained linear quadratic optimal control problems," Computational Optimization and Applications, Springer, vol. 51(2), pages 867-882, March.
    2. Matthias Gerdts & Martin Kunkel, 2011. "A globally convergent semi-smooth Newton method for control-state constrained DAE optimal control problems," Computational Optimization and Applications, Springer, vol. 48(3), pages 601-633, April.
    3. M. Gerdts, 2006. "Representation of the Lagrange Multipliers for Optimal Control Problems Subject to Differential-Algebraic Equations of Index Two," Journal of Optimization Theory and Applications, Springer, vol. 130(2), pages 231-251, August.

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