Discrete optimal control: the accessory problem and necessary optimality conditions

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Authors

HILSCHER Roman ZEIDAN Vera

Year of publication 2000
Type Article in Periodical
Magazine / Source Journal of Mathematical Analysis and Applications
MU Faculty or unit

Faculty of Science

Citation
Field General mathematics
Keywords discrete maximum principle; discrete Hamiltonian system; discrete quadratic functional; accesory problem; optimality conditions; Jacobi system; conjugate interval; controllability
Description In this work we derive the accessory problem for a general nonlinear discrete optimal control problem. We obtain necessary conditions for optimality -- nonnegativity of the second variation. As the second variation is a discrete quadratic functional, we proceed by deriving necessary conditions for the nonnegativity of such functionals. Certain controllability (or normality) assumption is required.
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