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

• Published in: Journal of optimization theory and applications Vol. 130; no. 3; pp. 443 - 462
• Main Author: Gerdts, M.
• Format: Journal Article
• Language: English
• Published: New York, NY Springer 01.09.2006; Springer Nature B.V
• Subjects: Algebra; Applied sciences; Banach spaces; Differential equations; Exact sciences and technology; Lagrange multiplier; Mathematical analysis; Mathematical models; Mathematical programming; Multipliers; Operational research and scientific management; Operational research. Management science; Optimal control; Optimization; Optimization techniques; Ordinary differential equations; Principles; Regularity; Representations; Studies; Mixed state; Differential equation; Differential system; index two differential-algebraic equations; state constraints; Optimization; Control constraint; Qualification; Equations of state; Algebraic system; necessary conditions; Optimal control; Algebraic equation; Multiplier; Minimum principle; local minimum principle; Optimality condition; Optimality criterion; Regularity; State constraint
• ISSN: 0022-3239; 1573-2878
• DOI: 10.1007/s10957-006-9121-9

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. [PUBLICATION ABSTRACT]