Javier F Rosenblueth, "Rank Assumptions for the Legendre-Clebsch Condition in Optimal Control," WSEAS Transactions on Systems, vol. 25, pp. 106-115, 2026, DOI:10.37394/23202.2026.25.10
Javier F Rosenblueth. Rank Assumptions for the Legendre-Clebsch Condition in Optimal Control.
WSEAS Transactions on Systems. 2026;25:106-115. 10.37394/23202.2026.25.10
WSEAS Transactions on Systems
Print ISSN: 1109-2777, E-ISSN: 2224-2678
Volume 25, 2026
Rank Assumptions for the Legendre-Clebsch Condition in Optimal Control
Author:
Abstract: For optimal control problems involving mixed equality and inequality constraints, and allowing the
endpoints to vary, different rank assumptions are studied in order to obtain the Legendre-Clebsch necessary
condition of optimality. A direct proof is given, taking into account the multipliers associated with the extremal
under consideration, without imposing the standard nondegeneracy condition on the full rank of the matrix of
gradients of active constraints. This weaker assumption allows us to enlarge its range of applicability.
Keywords:
Optimal control, Legendre-Clebsch necessary condition, equality and inequality constraints, mathematical programming, normality, calculus of variations
Pages: 106-115 WSEAS Transactions on Systems, ISSN / E-ISSN: 1109-2777 / 2224-2678, Volume 25, 2026, Art. #10 DOI: 10.37394/23202.2026.25.10
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