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An invariant second variation in optimal control. (English) Zbl 0945.49015
Summary: For an optimal control problem we define a second variation which is invariant under change of coordinates, and realize it as a linear-quadratic problem. When the strong Legendre condition is satisfied we give a complete Hamiltonian characterization of the index and of the nullity of the second variation.

49K15 Optimality conditions for problems involving ordinary differential equations
49N10 Linear-quadratic optimal control problems
49K27 Optimality conditions for problems in abstract spaces
58E25 Applications of variational problems to control theory
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