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

M. Gerdts
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M. Gerdts: University of Hamburg

Journal of Optimization Theory and Applications, 2006, vol. 130, issue 3, No 4, 443-462

Abstract: 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.

Keywords: Optimal control; necessary conditions; local minimum principle; index two differential-algebraic equations; state constraints (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1007/s10957-006-9121-9

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