WSEAS Transactions on Systems and Control
Print ISSN: 1991-8763, E-ISSN: 2224-2856
Volume 10, 2015
Modified Critical Directions for Inequality Control Constraints
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Abstract: For optimal control problems involving equality and inequality constraints in the control functions, some fundamental questions related to second order necessary conditions are posed. In particular, for a wide range of problems, we provide a direct derivation of such conditions in terms of a certain quadratic function, under some normality assumptions, and on a specific convex set of differentially admissible variations defining the critical directions. The question of whether this result can be improved by weakening the assumptions and modifying the set of critical directions by enlarging it is also studied. Under certain assumptions, an affirmative answer to that question is provided.
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Keywords: Optimal control, second order conditions, equality and/or inequality constraints, regularity
Pages: 215-227
WSEAS Transactions on Systems and Control, ISSN / E-ISSN: 1991-8763 / 2224-2856, Volume 10, 2015, Art. #24